Центральная предельная теорема для неоднородных цепей Маркова. I
Р. Л. Добрушин

Эта публикация цитируется в следующих статьяx:

1. John C. Duchi, Feng Ruan, “The right complexity measure in locally private estimation: It is not the Fisher information”, Ann. Statist., 52:1 (2024)  
2. Giulia De Pasquale, Kevin D. Smith, Francesco Bullo, Maria Elena Valcher, “Dual Seminorms, Ergodic Coefficients and Semicontraction Theory”, IEEE Trans. Automat. Contr., 69:5 (2024), 3040  
3. Elena Ghazi, Ibrahim Issa, “Total Variation Meets Differential Privacy”, IEEE J. Sel. Areas Inf. Theory, 5 (2024), 207  
4. William Lu, Anuran Makur, Japneet Singh, 2024 IEEE International Symposium on Information Theory (ISIT), 2024, 2544  
5. Robinson D. H. Cung, Yanina Y. Shkel, Ibrahim Issa, 2024 IEEE International Symposium on Information Theory (ISIT), 2024, 2748  
6. Julien Béguinot, Wei Cheng, Sylvain Guilley, Olivier Rioul, Lecture Notes in Computer Science, 14925, Advances in Cryptology – CRYPTO 2024, 2024, 389  
7. Patrick A. Imam, Jonathan R.W. Temple, “Political institutions and output collapses”, European Journal of Political Economy, 85 (2024), 102573  
8. Yunus Emre Demirci, Ali Devran Kara, Serdar Yüksel, 2024 American Control Conference (ACC), 2024, 3909  
9. Qian Qin, “Analysis of two-component Gibbs samplers using the theory of two projections”, Ann. Appl. Probab., 34:5 (2024)  
10. Haiyan Zhang, Xinghua Li, Mengfan Xu, Ximeng Liu, Tong Wu, Jian Weng, Robert H. Deng, “BADFL: Backdoor Attack Defense in Federated Learning From Local Model Perspective”, IEEE Trans. Knowl. Data Eng., 36:11 (2024), 5661  
11. Xin Guo, Yonghui Huang, Yi Zhang, “On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces”, Mathematics of OR, 2024  
12. Satvik Singh, Nilanjana Datta, Ion Nechita, “Ergodic theory of diagonal orthogonal covariant quantum channels”, Lett Math Phys, 114:5 (2024)  
13. Yunus Emre Demirci, Ali Devran Kara, Serdar Yüksel, “Average Cost Optimality of Partially Observed MDPs: Contraction of Nonlinear Filters and Existence of Optimal Solutions and Approximations”, SIAM J. Control Optim., 62:6 (2024), 2859  
14. Agbedeyi, O. D., Maliki, S. O., Asor, V. E., “A Predictive Model for Digital Currencies Prices using Geometric Brownian Motion Stochastic Differential Equation: A Case Study of the Bitcoin”, African Journal of Mathematics and Statistics Studies, 7:4 (2024), 188  
15. Adalberto J. A. Tavares Jr., Neusa M. F. Oliveira, “A Novel Approach for Kalman Filter Tuning for Direct and Indirect Inertial Navigation System/Global Navigation Satellite System Integration”, Sensors, 24:22 (2024), 7331  
16. Dongmin Lee, Anuran Makur, 2024 60th Annual Allerton Conference on Communication, Control, and Computing, 2024, 1  
17. Liam Cregg, Tamás Linder, Serdar Yüksel, “Reinforcement Learning for Near-Optimal Design of Zero-Delay Codes for Markov Sources”, IEEE Trans. Inform. Theory, 70:11 (2024), 8399  
18. Ю. А. Альпин, Н. Н. Корнеева, “Коэффициент эргодичности. Новые доказательства известных свойств”, Матем. заметки, 114:6 (2023), 803–807    ; Yu. A. Alpin, N. N. Korneeva, “Ergodicity Coefficient. New Proofs of Known Properties”, Math. Notes, 114:6 (2023), 1103–1106  
19. Yeor Hafouta, “Convergence rates in the functional CLT for α-mixing triangular arrays”, Stochastic Processes and their Applications, 161 (2023), 242  
20. Ari Arapostathis, Serdar Yüksel, “Convex analytic method revisited: Further optimality results and performance of deterministic policies in average cost stochastic control”, Journal of Mathematical Analysis and Applications, 517:2 (2023), 126567  
21. Pierre Del Moral, Emma Horton, Ajay Jasra, “On the stability of positive semigroups”, Ann. Appl. Probab., 33:6A (2023)  
22. Mengmei Xi, Chunhua Wang, Xuejun Wang, “Uniformly strong consistency and the rates of asymptotic normality for the edge frequency polygons”, Statistics, 57:6 (2023), 1444  
23. Abdessatar Souissi, El Gheteb Soueidy, Abdessatar Barhoumi, “On a ψ-Mixing property for Entangled Markov Chains”, Physica A: Statistical Mechanics and its Applications, 613 (2023), 128533  
24. Manon Baudel, Arnaud Guyader, Tony Lelièvre, “On the Hill relation and the mean reaction time for metastable processes”, Stochastic Processes and their Applications, 155 (2023), 393  
25. Jie Chen, Xiang Li, “Toward the minimum vertex cover of complex networks using distributed potential games”, Sci. China Inf. Sci., 66:1 (2023)  
26. Anirban Mondal, Kai Yin, Abhijit Mandal, “A two-stage adaptive Metropolis algorithm”, Journal of Statistical Computation and Simulation, 93:7 (2023), 1130  
27. Jean-René Chazottes, Sandro Gallo, Daniel Y. Takahashi, “Gaussian concentration bounds for stochastic chains of unbounded memory”, Ann. Appl. Probab., 33:5 (2023)  
28. А. Ю. Веретенников, М. А. Веретенникова, “Об улучшенных оценках и условиях сходимости для цепей Маркова”, Изв. РАН. Сер. матем., 86:1 (2022), 98–133          ; A. Yu. Veretennikov, M. A. Veretennikova, “On improved bounds and conditions for the convergence of Markov chains”, Izv. Math., 86:1 (2022), 92–125    
29. Jin Xu, Weiqi Wang, Zheming Gao, Haochen Luo, Qian Wu, “A Novel Markov Model for Near-Term Railway Delay Prediction”, SSRN Journal, 2022  
30. Chenlu Zhuansun, Gongxuan Zhang, Kedong Yan, “Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors”, Mathematica Slovaca, 72:3 (2022), 797  
31. Ali Devran Kara, Serdar Yüksel, “Convergence of Finite Memory Q Learning for POMDPs and Near Optimality of Learned Policies Under Filter Stability”, Mathematics of OR, 2022  
32. Eva-Maria Infanger, Gerald Infanger, Zsolt Lavicza, Florian Sobieczky, Communications in Computer and Information Science, 1633, Database and Expert Systems Applications - DEXA 2022 Workshops, 2022, 11  
33. Li Gao, Cambyse Rouzé, “Complete Entropic Inequalities for Quantum Markov Chains”, Arch Rational Mech Anal, 245:1 (2022), 183  
34. Vladimir R. Kostic, Ernest Sanca, Dragana Lj. Cvetkovic, 2022 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), 2022, 1  
35. Nachi Avraham-Re'em, “On absolutely continuous invariant measures and Krieger-type of Markov subshifts”, JAMA, 147:1 (2022), 201  
36. Ali Devran Kara, Erhan Bayraktar, Serdar Yuksel, 2022 IEEE 61st Conference on Decision and Control (CDC), 2022, 2301  
37. Pingyan Chen, Soo Hak Sung, “A Marcinkiewicz-Zygmund type strong law for weighted sums of φ-mixing random variables and its applications”, Journal of Mathematical Analysis and Applications, 505:1 (2022), 125572  
38. Pradeep Kr. Banerjee, Kedar Karhadkar, Yu Guang Wang, Uri Alon, Guido Montufar, 2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2022, 1  
39. Mert Kayaalp, Virginia Bordignon, Stefan Vlaski, Ali H. Sayed, 2022 IEEE Data Science and Learning Workshop (DSLW), 2022, 1  
40. Zhengliang Lu, Shengnan Ding, Fei Zhang, Rui Wang, Xuejun Wang, “The consistency and convergence rate for the nearest neighbor density estimator based on φ-mixing random samples”, Communications in Statistics - Theory and Methods, 51:3 (2022), 669  
41. Curtis McDonald, Serdar Yüksel, “Robustness to Incorrect Priors and Controlled Filter Stability in Partially Observed Stochastic Control”, SIAM J. Control Optim., 60:2 (2022), 842  
42. Michael Dikshtein, Nir Weinberger, Shlomo Shamai Shitz, 2022 IEEE International Symposium on Information Theory (ISIT), 2022, 2475  
43. Jan Haskovec, “Asymptotic behavior of the linear consensus model with delay and anticipation”, Math Methods in App Sciences, 45:16 (2022), 9979  
44. Dmitry Dolgopyat, Yeor Hafouta, “Edgeworth expansions for independent bounded integer valued random variables”, Stochastic Processes and their Applications, 152 (2022), 486  
45. Jan Haskovec, “A Simple Proof of Asymptotic Consensus in the Hegselmann–Krause and Cucker–Smale Models with Normalization and Delay”, SIAM J. Appl. Dyn. Syst., 20:1 (2021), 130  
46. Ali Devran Kara, Serdar Yuksel, 2021 60th IEEE Conference on Decision and Control (CDC), 2021, 1603  
47. Matthew C. Ledwith, Ross A. Jackson, Amanda M. Reboulet, Thomas P. Talafuse, Research Anthology on Military and Defense Applications, Utilization, Education, and Ethics, 2021, 92  
48. NAZIFE ERKURŞUN-ÖZCAN, FARRUKH MUKHAMEDOV, “SPECTRAL CONDITIONS FOR UNIFORM P-ERGODICITIES OF MARKOV OPERATORS ON ABSTRACT STATES SPACES”, Glasgow Math. J., 63:3 (2021), 682  
49. Shahab Asoodeh, Maryam Aliakbarpour, Flavio P. Calmon, 2021 IEEE International Symposium on Information Theory (ISIT), 2021, 545  
50. Grégoire Ferré, Mathias Rousset, Gabriel Stoltz, “More on the long time stability of Feynman–Kac semigroups”, Stoch PDE: Anal Comp, 9:3 (2021), 630  
51. Luigi Accardi, Yun Gang Lu, Abdessatar Souissi, “A Markov–Dobrushin Inequality for Quantum Channels”, Open Syst. Inf. Dyn., 28:04 (2021)  
52. Farrukh Mukhamedov, Ahmed Al-Rawashdeh, “Approximations of non-homogeneous Markov chains on abstract states spaces”, Bull. Math. Sci., 11:03 (2021)  
53. Farrukh Mukhamedov, “A Few Remarks on Asymptotic Stabilities of Markov Operators on $\boldsymbol{L}^{\mathbf{1}}$-Spaces”, Lobachevskii J Math, 42:13 (2021), 3173  
54. Shahab Asoodeh, Wei-Ning Chen, Flavio P. Calmon, Ayfer Ozgur, 2021 IEEE International Symposium on Information Theory (ISIT), 2021, 344  
55. А. Макур, Л. Чжэн, “Сравнение коэффициентов сжатия для $f$-дивергенций”, Пробл. передачи информ., 56:2 (2020), 3–63    ; A. Makur, L. Zheng, “Comparison of contraction coefficients for $f$-divergences”, Problems Inform. Transmission, 56:2 (2020), 103–156      
56. Erkursun-ozcan N., Mukhamedov F., “Stability Estimates of Markov Semigroups on Abstract States Spaces”, Mediterr. J. Math., 17:2 (2020), 44    
57. Mukhamedov F., Al-Rawashdeh A., “Generalized Dobrushin Ergodicity Coefficient and Uniform Ergodicities of Markov Operators”, Positivity, 24:4 (2020), 855–890    
58. А. Ю. Веретенников, М. А. Веретенникова, “О скорости сходимости для однородных цепей Маркова”, Докл. РАН. Матем., информ., проц. упр., 490 (2020), 16–19      ; A. Yu. Veretennikov, M. A. Veretennikova, “On convergence rates for homogeneous Markov chains”, Dokl. Math., 101:1 (2020), 12–15  
59. Anuran Makur, Elchanan Mossel, Yury Polyanskiy, “Broadcasting on Random Directed Acyclic Graphs”, IEEE Trans. Inform. Theory, 66:2 (2020), 780  
60. P. -C. G. Vassiliou, “Rate of Convergence and Periodicity of the Expected Population Structure of Markov Systems that Live in a General State Space”, Mathematics, 8:6 (2020), 1021  
61. Curtis McDonald, Serdar Yüksel, “Exponential filter stability via Dobrushin's coefficient”, Electron. Commun. Probab., 25:none (2020)  
62. Zahra Askarzadeh, Rui Fu, Abhishek Halder, Yongxin Chen, Tryphon T. Georgiou, “Stability Theory of Stochastic Models in Opinion Dynamics”, IEEE Trans. Automat. Contr., 65:2 (2020), 522  
63. Dario Fasino, Francesco Tudisco, “Ergodicity Coefficients for Higher-Order Stochastic Processes”, SIAM Journal on Mathematics of Data Science, 2:3 (2020), 740  
64. Dan Crisan, Alberto López-Yela, Joaquin Miguez, “Stable Approximation Schemes for Optimal Filters”, SIAM/ASA J. Uncertainty Quantification, 8:1 (2020), 483  
65. Shahab Asoodeh, Mario Diaz, Flavio P. Calmon, 2020 IEEE International Symposium on Information Theory (ISIT), 2020, 896  
66. Takashi Kamihigashi, John Stachurski, “A unified stability theory for classical and monotone Markov chains”, J. Appl. Probab., 56:01 (2019), 1  
67. Constantinos Daskalakis, Nishanth Dikkala, Gautam Kamath, “Testing Ising Models”, IEEE Trans. Inform. Theory, 65:11 (2019), 6829  
68. Bora Yongacoglu, Gurdal Arslan, Serdar Yuksel, 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, 5556  
69. Matthew C. Ledwith, Ross A. Jackson, Amanda M. Reboulet, Thomas P. Talafuse, “Ethics and Education”, International Journal of Responsible Leadership and Ethical Decision-Making, 1:1 (2019), 25  
70. Kalyan Santra, Emily A. Smith, Xueyu Song, Jacob W. Petrich, “A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments”, Photochem & Photobiology, 95:3 (2019), 773  
71. Grégoire Ferré, Gabriel Stoltz, “Error estimates on ergodic properties of discretized Feynman–Kac semigroups”, Numer. Math., 143:2 (2019), 261  
72. Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236      
73. М. К. Долгалёва, Ю. С. Харин, “Асимптотический анализ статистических оценок параметров биномиальной условно авторегрессионной модели пространственно-временных данных”, Журн. Белорус. гос. ун-та. Матем. Инф., 2 (2018), 47–57  
74. Tatiana Tatarenko, “Independent Log-Linear Learning in Potential Games With Continuous Actions”, IEEE Trans. Control Netw. Syst., 5:3 (2018), 913  
75. Alessandro Arlotto, J. Michael Steele, “A Central Limit Theorem for Costs in Bulinskaya's Inventory Management Problem When Deliveries Face Delays”, Methodol Comput Appl Probab, 20:3 (2018), 839  
76. Anuran Makur, Yury Polyanskiy, “Comparison of Channels: Criteria for Domination by a Symmetric Channel”, IEEE Trans. Inform. Theory, 64:8 (2018), 5704  
77. Suling Kang, Rashid Abbasi, Huiling Wang, Lixiang Xu, Xiaofeng Wang, Yuanyan Tang, “Asymptotic behaviour of frequency polygons under φ-mixing samples”, Communications in Statistics - Theory and Methods, 47:21 (2018), 5369  
78. Flavio du Pin Calmon, Yury Polyanskiy, Yihong Wu, “Strong Data Processing Inequalities for Input Constrained Additive Noise Channels”, IEEE Trans. Inform. Theory, 64:3 (2018), 1879  
79. Michael Bromberg, Corinna Ulcigrai, “A temporal central limit theorem for real-valued cocycles over rotations”, Ann. Inst. H. Poincaré Probab. Statist., 54:4 (2018)  
80. János Engländer, Stanislav Volkov, “Turning a Coin over Instead of Tossing It”, J Theor Probab, 31:2 (2018), 1097  
81. Evangelos D. Spyrou, Dimitrios K. Mitrakos, Lecture Notes in Computer Science, 10517, Ad-hoc, Mobile, and Wireless Networks, 2017, 255  
82. Yury Polyanskiy, Yihong Wu, The IMA Volumes in Mathematics and its Applications, 161, Convexity and Concentration, 2017, 211  
83. Nazife Erkursun Özcan, Farrukh Mukhamedov, “Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces”, J. Phys.: Conf. Ser., 819 (2017), 012015  
84. Damjan Škulj, “Perturbation bounds and degree of imprecision for uniquely convergent imprecise Markov chains”, Linear Algebra and its Applications, 533 (2017), 336  
85. Ф. М. Мухамедов, М. А. Мухамедов, “Коэффициент эргодичности и эргодические свойства неоднородных цепей Маркова в упорядоченных нормированных пространствах с базой”, Матем. заметки, 99:3 (2016), 477–480        ; F. M. Mukhamedov, M. A. Mukhamedov, “Ergodicity Coefficient and Ergodic Properties of Inhomogeneous Markov Chains in Ordered Normed Spaces with a Base”, Math. Notes, 99:3 (2016), 480–483    
86. Arlotto A. Steele J.M., “A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming”, Math. Oper. Res., 41:4 (2016), 1448–1468    
87. Kody J. H. Law, Hamidou Tembine, Raul Tempone, “Deterministic Mean-Field Ensemble Kalman Filtering”, SIAM J. Sci. Comput., 38:3 (2016), A1251  
88. Yury Polyanskiy, Yihong Wu, “Dissipation of Information in Channels With Input Constraints”, IEEE Trans. Inform. Theory, 62:1 (2016), 35  
89. Yeor Hafouta, Yuri Kifer, “A Nonconventional Local Limit Theorem”, J Theor Probab, 29:4 (2016), 1524  
90. Fumio Hiai, Mary Beth Ruskai, “Contraction coefficients for noisy quantum channels”, Journal of Mathematical Physics, 57:1 (2016)  
91. Maxim Raginsky, “Strong Data Processing Inequalities and <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math> </inline-formula>-Sobolev Inequalities for Discrete Channels”, IEEE Trans. Inform. Theory, 62:6 (2016), 3355  
92. С. В. Нагаев, “Спектральный метод и эргодические теоремы для общих цепей Маркова”, Изв. РАН. Сер. матем., 79:2 (2015), 101–136            ; S. V. Nagaev, “The spectral method and ergodic theorems for general Markov chains”, Izv. Math., 79:2 (2015), 311–345    
93. Mukhamedov F., “Ergodic Properties of Nonhomogeneous Markov Chains Defined on Ordered Banach Spaces With a Base”, Acta Math. Hung., 147:2 (2015), 294–323    
94. Flavio P. Calmon, Yury Polyanskiy, Yihong Wu, 2015 IEEE International Symposium on Information Theory (ISIT), 2015, 2558  
95. Zbigniew S. Szewczak, “A moment maximal inequality for dependent random variables”, Statistics & Probability Letters, 106 (2015), 129  
96. Matthias Fugger, Thomas Nowak, Bernadette Charron-Bost, 2015 49th Annual Conference on Information Sciences and Systems (CISS), 2015, 1  
97. Oleg Butkovsky, “Subgeometric rates of convergence of Markov processes in the Wasserstein metric”, Ann. Appl. Probab., 24:2 (2014)  
98. P. C. G. Vassiliou, “Markov Systems in a General State Space”, Communications in Statistics - Theory and Methods, 43:7 (2014), 1322  
99. U. Narayan Bhat, Wiley StatsRef: Statistics Reference Online, 2014  
100. Xavier Bressaud, Alexander I. Bufetov, Pascal Hubert, “Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1”, Proceedings of the London Mathematical Society, 109:2 (2014), 483  
101. Sebastien Motsch, Eitan Tadmor, “Heterophilious Dynamics Enhances Consensus”, SIAM Rev., 56:4 (2014), 577  
102. Manuel E. Lladser, Stephen R. Chestnut, “Approximation of sojourn-times via maximal couplings: motif frequency distributions”, J. Math. Biol., 69:1 (2014), 147  
103. De-Mei Yuan, Xue-Mei Hu, Bao Tao, “SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES”, Journal of the Korean Mathematical Society, 51:3 (2014), 609  
104. О. А. Бутковский, “Об эргодических свойствах нелинейных марковских цепей и стохастических уравнений Маккина–Власова”, Теория вероятн. и ее примен., 58:4 (2013), 782–794        ; O. A. Butkovsky, “On ergodic properties of nonlinear Markov chains and stochastic McKean–Vlasov equations”, Theory Probab. Appl., 58:4 (2014), 661–674      
105. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 3  
106. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 141  
107. O.A. Butkovsky, A.Yu. Veretennikov, “On asymptotics for Vaserstein coupling of Markov chains”, Stochastic Processes and their Applications, 123:9 (2013), 3518  
108. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 59  
109. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 235  
110. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 285  
111. Bo Yang, Jin Di, Jiming Liu, Dayou Liu, “Hierarchical community detection with applications to real-world network analysis”, Data & Knowledge Engineering, 83 (2013), 20  
112. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 31  
113. S. V. Nagaev, “The ergodic theorems for Markov chains with an arbitrary phase space”, Dokl. Math., 88:3 (2013), 684  
114. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 319  
115. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 341  
116. Discrete‐time Asset Pricing Models in Applied Stochastic Finance, 2013, 365  
117. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 17  
118. Farrukh Mukhamedov, “On L 1-weak ergodicity of nonhomogeneous discrete Markov processes and its applications”, Rev Mat Complut, 26:2 (2013), 799  
119. Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler, “Discrete time markovian agents interacting through a potential”, ESAIM: PS, 17 (2013), 614  
120. G. George Yin, Qing Zhang, Stochastic Modelling and Applied Probability, 37, Continuous-Time Markov Chains and Applications, 2013, 261  
121. Farrukh Mukhamedov, “The Dobrushin ergodicity coefficient and the ergodicity of noncommutative Markov chains”, Journal of Mathematical Analysis and Applications, 408:1 (2013), 364  
122. Ю. А. Альпин, В. С. Альпина, “О нормальной форме стохастической матрицы”, Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки, 154, № 2, Изд-во Казанского ун-та, Казань, 2012, 60–72  
123. А. Ю. Веретенников, С. А. Клоков, “Об условиях локального перемешивания для аппроксимаций стохастических дифференциальных уравнений”, Теория вероятн. и ее примен., 57:1 (2012), 35–61          ; A. Yu. Veretennikov, S. A. Klokov, “On local mixing conditions for SDE approximations”, Theory Probab. Appl., 57:1 (2013), 110–131      
124. Zbigniew S. Szewczak, “On Dobrushin's inequality”, Statistics & Probability Letters, 82:6 (2012), 1202  
125. Steven Hecht Orzack, Ulrich K. Steiner, Shripad Tuljapurkar, Paul Thompson, “Static and dynamic expression of life history traits in the northern fulmar Fulmarus glacialis”, Oikos, 120:3 (2011), 369  
126. Mathieu Tracol, “Recurrence and transience for finite probabilistic tables”, Theoretical Computer Science, 412:12-14 (2011), 1154  
127. Richard C. Bradley, “A note on two measures of dependence”, Statistics & Probability Letters, 81:12 (2011), 1823  
128. Ilse C. F. Ipsen, Teresa M. Selee, “Ergodicity Coefficients Defined by Vector Norms”, SIAM J. Matrix Anal. & Appl., 32:1 (2011), 153  
129. Stephen J. Kirkland, Michael Neumann, “The case of equality in the Dobrushin–Deutsch–Zenger bound”, Linear Algebra and its Applications, 431:12 (2009), 2373  
130. Biman Chakraborty, Probal Chaudhuri, “On an Optimization Problem in Robust Statistics”, Journal of Computational and Graphical Statistics, 17:3 (2008), 683  
131. Alireza Tahbaz-Salehi, Ali Jadbabaie, “A Necessary and Sufficient Condition for Consensus Over Random Networks”, IEEE Trans. Automat. Contr., 53:3 (2008), 791  
132. A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. I”, Mosc. Math. J., 5:3 (2005), 679–704        
133. A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. II”, Mosc. Math. J., 5:4 (2005), 927–959        
134. U. Narayan Bhat, Encyclopedia of Statistical Sciences, 2005  
135. К. Декомб, Е. А. Жижина, “Применение методов теории гиббсовских случайных полей к задачам обработки изображений”, Пробл. передачи информ., 40:3 (2004), 108–125      ; X. Decombes, E. A. Zhizhina, “Application of Gibbs Random Fields Methods to Image Denoising Problems”, Problems Inform. Transmission, 40:3 (2004), 279–295  
136. M. Forrest Hill, Jon D. Witman, Hal Caswell, “Markov Chain Analysis of Succession in a Rocky Subtidal Community”, The American Naturalist, 164:2 (2004), E46  
137. U. Narayan Bhat, Encyclopedia of Statistical Sciences, 2004  
138. В. И. Оселедец, Д. В. Хмелёв, “Стохастические транспортные сети и устойчивость динамических систем”, Теория вероятн. и ее примен., 46:1 (2001), 147–154      ; V. I. Oseledets, D. V. Khmelev, “Stochastic Transportation Networks and Stability of Dynamical Systems”, Theory Probab. Appl., 46:1 (2002), 154–161    
139. P. Del Moral, M. Kouritzin, L. Miclo, “On a Class of Discrete Generation Interacting Particle Systems”, Electron. J. Probab., 6:none (2001)  
140. Grace E. Cho, Carl D. Meyer, “Comparison of perturbation bounds for the stationary distribution of a Markov chain”, Linear Algebra and its Applications, 335:1-3 (2001), 137  
141. J. Sunklodas, Limit Theorems of Probability Theory, 2000, 113  
142. Xavier Bressaud, Roberto Fernández, Antonio Galves, “Speed of d-convergence for Markov approximations of chains with complete connections. A coupling approach”, Stochastic Processes and their Applications, 83:1 (1999), 127  
143. И. А. Ибрагимов, “Работы Р. Л. Добрушина о процессах Маркова”, УМН, 52:2(314) (1997), 5–9          ; I. A. Ibragimov, “Dobrushin's works on Markov processes”, Russian Math. Surveys, 52:2 (1997), 239–243    
144. G. Yin, Q. Zhang, 2, Proceedings of the 36th IEEE Conference on Decision and Control, 1997, 1103  
145. George Ch. Pflug, The Kluwer International Series in Engineering and Computer Science, 373, Optimization of Stochastic Models, 1996, 55  
146. Choon Peng Tan, “On the weak ergodicity of nonhomogeneous Markov chains”, Statistics & Probability Letters, 26:4 (1996), 293  
147. I. Fleischer, A. Joffe, “Preservation of ergodicity under perturbation”, Math Z, 218:1 (1995), 219  
148. I. Fleischer, A. Joffe, “Ratio ergodicity for non-homogeneous Markov Chains in general state spaces”, J Theor Probab, 8:1 (1995), 31  
149. N. I. Chernov, “Limit theorems and Markov approximations for chaotic dynamical systems”, Probab. Th. Rel. Fields, 101:3 (1995), 321  
150. Laurent Miclo, “Remarques sur l'ergodicité des algorithmes de recuit simulé sur un graphe”, Stochastic Processes and their Applications, 58:2 (1995), 329  
151. N. Giesbrecht, “Bounds for sums of random variables over a Markov chain”, Stochastic Processes and their Applications, 53:2 (1994), 269  
152. M. N. M. Van Lieshout, “Stochastic annealing for nearest-neighbour point processes with application to object recognition”, Advances in Applied Probability, 26:2 (1994), 281  
153. M. N. M. Van Lieshout, “Stochastic annealing for nearest-neighbour point processes with application to object recognition”, Adv. Appl. Probab., 26:02 (1994), 281  
154. Joel E. Cohen, Yoh Iwasa, Gh. Rautu, Mary Beth Ruskai, Eugene Seneta, Gh. Zbaganu, “Relative entropy under mappings by stochastic matrices”, Linear Algebra and its Applications, 179 (1993), 211  
155. D.J. Hartcfiel, “Cyclic markov set-chains”, Journal of Statistical Computation and Simulation, 46:3-4 (1993), 145  
156. G. Ch. Pflug, W. Schachermayer, “Coefficients of ergodicity for stochastically monotone Markov chains”, J. Appl. Probab., 29:04 (1992), 850  
157. G. Ch. Pflug, W. Schachermayer, “Coefficients of ergodicity for stochastically monotone Markov chains”, Journal of Applied Probability, 29:4 (1992), 850  
158. O. Catoni, Lecture Notes in Control and Information Sciences, 177, Applied Stochastic Analysis, 1992, 74  
159. Shiro Ishikawa, Roger D. Nussbaum, “Some remarks on differential equations of quadratic type”, J Dyn Diff Equat, 3:3 (1991), 457  
160. Gerhard Winkler, “An ergodic L2-theorem for simulated annealing in bayesian image reconstruction”, Journal of Applied Probability, 27:4 (1990), 779  
161. Gerhard Winkler, “An ergodic L 2-theorem for simulated annealing in bayesian image reconstruction”, J. Appl. Probab., 27:04 (1990), 779  
162. L. Heinrich, “A method for the derivation of limit theorems for sums of weakly dependent random variables:a survey”, Optimization, 18:5 (1987), 715  
163. R. Dwyer, L. Kurz, “Characterizing partition detectors with stationary and quasi-stationary Markov dependent data”, IEEE Trans. Inform. Theory, 32:4 (1986), 471  
164. Debasis Mitra, Fabio Romeo, Alberto Sangiovanni-Vincentelli, “Convergence and finite-time behavior of simulated annealing”, Advances in Applied Probability, 18:3 (1986), 747  
165. Debasis Mitra, Fabio Romeo, Alberto Sangiovanni-Vincentelli, “Convergence and finite-time behavior of simulated annealing”, Adv. Appl. Probab., 18:03 (1986), 747  
166. D. McDonald, “An invariance principle for semi-Markov processes”, Advances in Applied Probability, 17:1 (1985), 100  
167. Basilis Gidas, “Nonstationary Markov chains and convergence of the annealing algorithm”, J Stat Phys, 39:1-2 (1985), 73  
168. Norbert Herrndorf, “First-passage percolation processes with finite height”, Journal of Applied Probability, 22:4 (1985), 766  
169. Debasis Mitra, Fabio Romeo, Alberto Sangiovanni-Vincentelli, 1985 24th IEEE Conference on Decision and Control, 1985, 761  
170. D. McDonald, “An invariance principle for semi-Markov processes”, Adv. Appl. Probab., 17:01 (1985), 100  
171. Norbert Herrndorf, “First-passage percolation processes with finite height”, J. Appl. Probab., 22:04 (1985), 766  
172. С. М. Лозинский, “К столетию со дня рождения С. Н. Бернштейна”, УМН, 38:3(231) (1983), 191–203        ; S. M. Lozinskii, “On the hundredth anniversary of the birth of S. N. Bernstein”, Russian Math. Surveys, 38:3 (1983), 163–178    
173. R.N. Bhattacharya, S. Ramasubramanian, “Recurrence and ergodicity of diffusions”, Journal of Multivariate Analysis, 12:1 (1982), 95  
174. R. N. Bhattacharya, Springer Series in Synergetics, 8, Stochastic Nonlinear Systems in Physics, Chemistry, and Biology, 1981, 86  
175. Martingale Limit Theory and its Application, 1980, 285  
176. E. Seneta, “Coefficients of ergodicity: structure and applications”, Advances in Applied Probability, 11:3 (1979), 576  
177. E. Seneta, “Coefficients of ergodicity: structure and applications”, Adv. Appl. Probab., 11:03 (1979), 576  
178. Dean Isaacson, Richard L. Tweedie, “Criteria for strong ergodicity of Markov chains”, J. Appl. Probab., 15:01 (1978), 87  
179. Dean Isaacson, Barry Arnold, “Strong ergodicity for continuous-time Markov chains”, Journal of Applied Probability, 15:4 (1978), 699  
180. Б. А. Лифшиц, “О центральной предельной теореме для сумм случайных величин, связанных в цепь”, Теория вероятн. и ее примен., 23:2 (1978), 295–312  ; В. A. Lifšic, “On the central limit theorem for Markov chains”, Theory Probab. Appl., 23:2 (1979), 279–296    
181. Dean Isaacson, Glenn R. Luecke, “Strongly ergodic Markov chains and rates of convergence using spectral conditions”, Stochastic Processes and their Applications, 7:1 (1978), 113  
182. Dean Isaacson, Richard L. Tweedie, “Criteria for strong ergodicity of Markov chains”, Journal of Applied Probability, 15:1 (1978), 87  
183. Bo Lindqvist, “A decision theoretical characterization of weak ergodicity”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 44:2 (1978), 155  
184. Dean Isaacson, Barry Arnold, “Strong ergodicity for continuous-time Markov chains”, J. Appl. Probab., 15:04 (1978), 699  
185. Joel E. Cohen, “Ergodicity of age structure in populations with Markovian vital rates. II. General states”, Advances in Applied Probability, 9:1 (1977), 18  
186. З. И. Бежаева, “Условные цепи Маркова со счетным множеством состояний”, Теория вероятн. и ее примен., 22:3 (1977), 556–565  ; Z. I. Bežaeva, “Conditional Markov chains with denumerable set of states”, Theory Probab. Appl., 22:3 (1978), 543–553    
187. Joel E. Cohen, “Ergodicity of age structure in populations with Markovian vital rates. II. General states”, Adv. Appl. Probab., 9:01 (1977), 18  
188. Richard W. Madsen, “Decidability of α (pk) > 0 for some k”, J. Appl. Probab., 12:02 (1975), 333  
189. David Griffeath, “Uniform coupling of non-homogeneous Markov chains”, Journal of Applied Probability, 12:4 (1975), 753  
190. Richard W. Madsen, “Decidability of α (pk) > 0 for some k”, Journal of Applied Probability, 12:2 (1975), 333  
191. Б. А. Лифшиц, “О сходимости моментов в центральной предельной теореме для неоднородных цепей Маркова”, Теория вероятн. и ее примен., 20:4 (1975), 755–771  ; В. A. Lifšic, “Convergence of moments in the central limit theorem for nonstationary Markov chains”, Theory Probab. Appl., 20:4 (1976), 741–758    
192. J. F. C. Kingman, “Geometrical aspects of the theory of non-homogeneous Markov chains”, Math. Proc. Camb. Phil. Soc., 77:1 (1975), 171  
193. David Griffeath, “Uniform coupling of non-homogeneous Markov chains”, J. Appl. Probab., 12:04 (1975), 753  
194. И. В. Евстигнеев, “Положительные матричные коциклы над динамическими системами”, УМН, 29:5(179) (1974), 219–220      
195. Dean L. Isaacson, Richard W. Madsen, “L 1 ergodic behavior of non-negative kernels”, Israel J. Math., 17:4 (1974), 350  
196. З. И. Бежаева, “Эргодические свойства условных цепей Маркова”, Теория вероятн. и ее примен., 19:3 (1974), 547–557  ; Z. I. Bezhaeva, “Ergodicity properties of conditional Markov chains”, Theory Probab. Appl., 19:3 (1975), 522–531    
197. E. Seneta, “On the historical development of the theory of finite inhomogeneous Markov chains”, Math. Proc. Camb. Phil. Soc., 74:3 (1973), 507  
198. Ю. А. Давыдов, “Условия перемешивания для цепей Маркова”, Теория вероятн. и ее примен., 18:2 (1973), 321–338  ; Yu. A. Davydov, “Mixing Conditions for Markov Chains”, Theory Probab. Appl., 18:2 (1973), 312–328    
199. Introduction to Probabilistic Automata, 1971, 199  
200. J. R. Blum, M. Reichaw, “Two integral inequalities”, Israel J. Math., 9:1 (1971), 20  
201. M. Iosifescu, “Закон повторного логарифма для одного класса зависимых случайных величин”, Теория вероятн. и ее примен., 13:2 (1968), 315–325  ; M. Iosifescu, “The law of the iterated logarithm for a class of dependent random variables.”, Theory Probab. Appl., 13:2 (1968), 304–313    
202. A. Paz, 9th Annual Symposium on Switching and Automata Theory (swat 1968), 1968, 42  
203. И. А. Ибрагимов, “Центральная предельная теорема для одного класса зависимых случайных величин”, Теория вероятн. и ее примен., 8:1 (1963), 89–94  ; I. A. Ibragimov, “A Central Limit Theorem for a Class of Dependent Random Variables”, Theory Probab. Appl., 8:1 (1963), 83–89    
204. И. А. Ибрагимов, “Некоторые предельные теоремы для стационарных процессов”, Теория вероятн. и ее примен., 7:4 (1962), 361–392  ; I. A. Ibragimov, “Some Limit Theorems for Stationary Processes”, Theory Probab. Appl., 7:4 (1962), 349–382    
205. С. В. Нагаев, “Некоторые предельные теоремы для однородных цепей Маркова”, Теория вероятн. и ее примен., 2:4 (1957), 389–416  ; S. V. Nagaev, “Some Limit Theorems for Stationary Markov Chains”, Theory Probab. Appl., 2:4 (1957), 378–406    
206. “Резюме докладов, сделанных на заседаниях научно-исследовательского семинара по теории вероятностей (Москва, февраль – май 1957 г.)”, Теория вероятн. и ее примен., 2:4 (1957), 478–488  ; “Summary of Papers Presented at the Sessions of the Scientific Research Seminar on Probability Theory (Moscow, February–May, 1957)”, Theory Probab. Appl., 2:4 (1957), 470–480