RUS  ENG
Полная версия
ЖУРНАЛЫ // Теория вероятностей и ее применения

Теория вероятн. и ее примен., 1956, том 1, выпуск 4, страницы 365–425 (Mi tvp5010)

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

Эта публикация цитируется в следующих статьяx:
  1. O. Deniz Akyildiz, Pierre Del Moral, Joaquin Miguez, “On the contraction properties of Sinkhorn semigroups”, FoDS, 2026  crossref
  2. Nazife Erkurşun-Özcan, Farrukh Mukhamedov, “Residualities and uniform ergodicities of Markov semigroups”, Ann. Funct. Anal., 16:1 (2025)  crossref
  3. Imon Banerjee, Harsha Honnappa, Vinayak Rao, “Off-line Estimation of Controlled Markov Chains: Minimaxity and Sample Complexity”, Operations Research, 2025  crossref
  4. Fabián González, O. Deniz Akyildiz, Dan Crisan, Joaquín Míguez, “Nudging state-space models for Bayesian filtering under misspecified dynamics”, Stat Comput, 35:4 (2025)  crossref
  5. Liwang Ding, Ping Chen, “Uniform strong consistency of histogram density estimation for φ -mixing samples”, Communications in Statistics - Simulation and Computation, 53:2 (2024), 1037  crossref
  6. Wenzhi Yang, Ran Ding, Shuhe Hu, Chunyu Yao, “Exact laws of large numbers for k -th order statistics from the asymmetrical Cauchy distribution”, Communications in Statistics - Theory and Methods, 53:8 (2024), 2757  crossref
  7. P.-C.G. Vassiliou, “Weak Ergodicity in G-NHMS”, Methodol Comput Appl Probab, 26:3 (2024)  crossref
  8. Ahmed Ait Ameur, Hichem Elmossaoui, Nadia Oukid, “New Computer Experiment Designs with Area-Interaction Point Processes”, Mathematics, 12:15 (2024), 2397  crossref
  9. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 137  crossref
  10. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 113  crossref
  11. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 273  crossref
  12. Xin Deng, Yi Wu, Wei Wang, Xuejun Wang, “Asymptotic properties of M estimators in classical linear models with φ -mixing random errors”, Journal of Statistical Computation and Simulation, 93:18 (2023), 3259  crossref
  13. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 47  crossref
  14. Adel Aghajan, Behrouz Touri, “Distributed Optimization Over Dependent Random Networks”, IEEE Trans. Automat. Contr., 68:8 (2023), 4812  crossref
  15. Geoffrey Wolfer, “Empirical and instance‐dependent estimation of Markov chain and mixing time”, Scandinavian J Statistics, 2023  crossref
  16. Florence Merlevède, Magda Peligrad, Progress in Probability, 80, High Dimensional Probability IX, 2023, 229  crossref
  17. Dmitry Dolgopyat, Yeor Hafouta, “A Berry–Esseen theorem and Edgeworth expansions for uniformly elliptic inhomogeneous Markov chains”, Probab. Theory Relat. Fields, 186:1-2 (2023), 439  crossref
  18. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 1  crossref
  19. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 13  crossref
  20. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 179  crossref
  21. Yeor Hafouta, “An almost sure invariance principle for some classes of non-stationary mixing sequences”, Statistics & Probability Letters, 193 (2023), 109728  crossref
  22. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 85  crossref
  23. Dmitry Dolgopyat, Omri M. Sarig, Lecture Notes in Mathematics, 2331, Local Limit Theorems for Inhomogeneous Markov Chains, 2023, 229  crossref
  24. А. Ю. Веретенников, М. А. Веретенникова, “Об улучшенных оценках и условиях сходимости для цепей Маркова”, Изв. РАН. Сер. матем., 86:1 (2022), 98–133  mathnet  crossref  mathscinet  zmath  adsnasa; A. Yu. Veretennikov, M. A. Veretennikova, “On improved bounds and conditions for the convergence of Markov chains”, Izv. Math., 86:1 (2022), 92–125  crossref  isi
  25. Bartoszek W. Beska M. Florek W., “Generalized Dobrushin Coefficients on Banach Spaces”, Bull. Iran Math. Soc., 48:4 (2022), 1691–1709  crossref  isi
  26. Farrukh Mukhamedov, Ahmed Al-Rawashdeh, “Generalized Dobrushin ergodicity coefficient and ergodicities of non-homogeneous Markov chains”, Banach J. Math. Anal., 16:1 (2022)  crossref
  27. Liwang Ding, Ping Chen, Li Yongming, “Statistical inference for a heteroscedastic regression model with φ-mixing errors”, Communications in Statistics - Simulation and Computation, 51:8 (2022), 4658  crossref
  28. Roy Cerqueti, Emilio De Santis, “Monte Carlo Markov chains constrained on graphs for a target with disconnected support”, Electron. J. Statist., 16:2 (2022)  crossref
  29. Bora Yongacoglu, Gurdal Arslan, Serdar Yuksel, “Decentralized Learning for Optimality in Stochastic Dynamic Teams and Games With Local Control and Global State Information”, IEEE Trans. Automat. Contr., 67:10 (2022), 5230  crossref
  30. Jin Xu, Weiqi Wang, Zheming Gao, Haochen Luo, Qian Wu, “A Novel Markov Model for Near-Term Railway Delay Prediction”, SSRN Journal, 2022  crossref
  31. Vitaliy Golomoziy, Springer Proceedings in Mathematics & Statistics, 408, Stochastic Processes, Statistical Methods, and Engineering Mathematics, 2022, 97  crossref
  32. Vitaliy Golomoziy, “Exponential moments of simultaneous hitting time for non-atomic Markov chains”, Glas. Mat. Ser. III, 57:1 (2022), 129  crossref
  33. Li Gao, Cambyse Rouzé, “Complete Entropic Inequalities for Quantum Markov Chains”, Arch Rational Mech Anal, 245:1 (2022), 183  crossref
  34. Nazife Erkurşun-Özcan, Farrukh Mukhamedov, “UNIFORM ERGODICITIES OF MARKOV SEMIGROUPS ON ABSTRACT STATES SPACES”, J Math Sci, 266:3 (2022), 448  crossref
  35. Yan Wang, Xiaoqin Li, Ling Chen, Minghui Wang, Xuejun Wang, “A note on the asymptotic properties of the estimators in a semiparametric regression model”, Communications in Statistics - Simulation and Computation, 51:2 (2022), 358  crossref
  36. Demian Pouzo, Zacharias Psaradakis, Martin Sola, “Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities”, ECTA, 90:4 (2022), 1681  crossref
  37. Erkursun-Ozcan N., Mukhamedov F., “Spectral Conditions For Uniform P-Ergodicities of Markov Operators on Abstract States Spaces”, Glasg. Math. J., 63:3 (2021), PII S0017089520000440, 682–696  crossref  isi
  38. Grégoire Ferré, Mathias Rousset, Gabriel Stoltz, “More on the long time stability of Feynman–Kac semigroups”, Stoch PDE: Anal Comp, 9:3 (2021), 630  crossref
  39. Aiting Shen, Xiang Li, Yajing Zhang, Yige Qiu, Xuejun Wang, “Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model”, Stochastics, 93:6 (2021), 868  crossref
  40. Farrukh Mukhamedov, “A Few Remarks on Asymptotic Stabilities of Markov Operators on $\boldsymbol{L}^{\mathbf{1}}$-Spaces”, Lobachevskii J Math, 42:13 (2021), 3173  crossref
  41. 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  crossref
  42. А. Ю. Веретенников, М. А. Веретенникова, “О скорости сходимости для однородных цепей Маркова”, Докл. РАН. Матем., информ., проц. упр., 490 (2020), 16–19  mathnet  zmath  elib; A. Yu. Veretennikov, M. A. Veretennikova, “On convergence rates for homogeneous Markov chains”, Dokl. Math., 101:1 (2020), 12–15  crossref
  43. Liwang Ding, Ping Chen, “Statistical estimation for heteroscedastic semiparametric regression model with random errors”, Journal of Nonparametric Statistics, 32:4 (2020), 940  crossref
  44. Juan Alberto Rojas Cruz, Iesus C. Diniz, “On Weak and Strong Ergodicity”, J Stat Theory Pract, 13:2 (2019)  crossref
  45. Grégoire Ferré, Gabriel Stoltz, “Error estimates on ergodic properties of discretized Feynman–Kac semigroups”, Numer. Math., 143:2 (2019), 261  crossref
  46. Florence Merlevède, Magda Peligrad, Sergey Utev, “Functional CLT for martingale-like nonstationary dependent structures”, Bernoulli, 25:4B (2019)  crossref
  47. 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  crossref
  48. Nazife Erkurşun Özcan, Farrukh Mukhamedov, “Uniform Ergodicity of Lotz–Räbiger Nets of Markov Operators on Abstract State Spaces”, Results Math, 73:1 (2018)  crossref
  49. Michael Bromberg, Corinna Ulcigrai, “A temporal central limit theorem for real-valued cocycles over rotations”, Ann. Inst. H. Poincaré Probab. Statist., 54:4 (2018)  crossref
  50. Nazife Erkurşun-Özcan, Farrukh Mukhamedov, “Uniform ergodicities and perturbation bounds of Markov chains on base norm spaces”, Quaestiones Mathematicae, 41:6 (2018), 863  crossref
  51. Evangelos D. Spyrou, Dimitrios K. Mitrakos, Lecture Notes in Computer Science, 10517, Ad-hoc, Mobile, and Wireless Networks, 2017, 255  crossref
  52. Mukhamedov F., “Uniform Stability and Weak Ergodicity of Nonhomogeneous Markov Chains Defined on Ordered Banach Spaces With a Base”, Positivity, 20:1 (2016), 135–153  crossref  isi
  53. Goetze F., Eliseeva Yu.S., Zaitsev A.Yu., “Arak?s inequalities for concentration functions and the Littlewood?Offord problem”, Dokl. Math., 93:2 (2016), 202–206  crossref  isi
  54. Fumio Hiai, Mary Beth Ruskai, “Contraction coefficients for noisy quantum channels”, Journal of Mathematical Physics, 57:1 (2016)  crossref
  55. 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  crossref
  56. Kody J. H. Law, Hamidou Tembine, Raul Tempone, “Deterministic Mean-Field Ensemble Kalman Filtering”, SIAM J. Sci. Comput., 38:3 (2016), A1251  crossref
  57. С. В. Нагаев, “Спектральный метод и эргодические теоремы для общих цепей Маркова”, Изв. РАН. Сер. матем., 79:2 (2015), 101–136  mathnet  crossref  mathscinet  zmath  adsnasa  elib; S. V. Nagaev, “The spectral method and ergodic theorems for general Markov chains”, Izv. Math., 79:2 (2015), 311–345  crossref  isi
  58. Mukhamedov F., “Ergodic Properties of Nonhomogeneous Markov Chains Defined on Ordered Banach Spaces With a Base”, Acta Math. Hung., 147:2 (2015), 294–323  crossref  isi
  59. Zbigniew S. Szewczak, “A moment maximal inequality for dependent random variables”, Statistics & Probability Letters, 106 (2015), 129  crossref
  60. Farrukh Mukhamedov, Nasir Ganikhodjaev, Lecture Notes in Mathematics, 2133, Quantum Quadratic Operators and Processes, 2015, 31  crossref
  61. Haitao Han, Zhiming Wang, Qing Zhou, “Consensus of complex network systems and ergodicity of Markov chains”, IET Control Theory &amp; Applications, 9:2 (2015), 184  crossref
  62. Manuel E. Lladser, Stephen R. Chestnut, “Approximation of sojourn-times via maximal couplings: motif frequency distributions”, J. Math. Biol., 69:1 (2014), 147  crossref
  63. Eugene Seneta, “Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924–2008)”, Communications in Statistics - Theory and Methods, 43:7 (2014), 1296  crossref
  64. 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  crossref
  65. X. Zeng, M. Anitescu, “Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems”, Applied Mathematics and Computation, 233 (2014), 507  crossref
  66. U. Narayan Bhat, Wiley StatsRef: Statistics Reference Online, 2014  crossref
  67. D. Škulj, R. Hable, “Coefficients of ergodicity for Markov chains with uncertain parameters”, Metrika, 76:1 (2013), 107  crossref
  68. Farrukh Mukhamedov, “On L 1-weak ergodicity of nonhomogeneous discrete Markov processes and its applications”, Rev Mat Complut, 26:2 (2013), 799  crossref
  69. Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler, “Discrete time markovian agents interacting through a potential”, ESAIM: PS, 17 (2013), 614  crossref
  70. Huilin Huang, “The Central Limit Theorem for th-Order Nonhomogeneous Markov Information Source”, Journal of Probability and Statistics, 2013 (2013), 1  crossref
  71. Farrukh Mukhamedov, “On Dobrushin Ergodicity Coefficient and weak ergodicity of Markov Chains on Jordan Algebras”, J. Phys.: Conf. Ser., 435 (2013), 012002  crossref
  72. 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  mathnet  crossref  mathscinet  zmath  elib; A. Yu. Veretennikov, S. A. Klokov, “On local mixing conditions for SDE approximations”, Theory Probab. Appl., 57:1 (2013), 110–131  crossref  isi  elib
  73. 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  mathnet
  74. Zbigniew S. Szewczak, “On Dobrushin's inequality”, Statistics & Probability Letters, 82:6 (2012), 1202  crossref
  75. Stephen Gundry, Elkin Urrea, Cem Safak Sahin, Jianmin Zou, M. Umit Uyar, 34th IEEE Sarnoff Symposium, 2011, 1  crossref
  76. Anirban DasGupta, Springer Texts in Statistics, Probability for Statistics and Machine Learning, 2011, 613  crossref
  77. Igor V. Evstigneev, Sergey A. Pirogov, “Stochastic nonlinear Perron–Frobenius theorem”, Positivity, 14:1 (2010), 43  crossref
  78. Cem Safak Sahin, Stephen Gundry, Elkin Urrea, M. Umit Uyar, Michael Conner, Giorgio Bertoli, Christian Pizzo, 2010 IEEE Sarnoff Symposium, 2010, 1  crossref
  79. Mahmud Akelbek, Steve Kirkland, “Coefficients of ergodicity and the scrambling index”, Linear Algebra and its Applications, 430:4 (2009), 1111  crossref
  80. Biman Chakraborty, Probal Chaudhuri, “On an Optimization Problem in Robust Statistics”, Journal of Computational and Graphical Statistics, 17:3 (2008), 683  crossref
  81. А. С. Маслов, “Оценка вероятности эргодичности таблицы разностей случайной подстановки”, Тр. Ин-та матем., 14:2 (2006), 86–94  mathnet
  82. А. Ю. Митрофанов, “Оценки устойчивости для конечных однородных цепей Маркова с непрерывным временем”, Теория вероятн. и ее примен., 50:2 (2005), 371–379  mathnet  crossref  mathscinet  zmath  elib; A. Yu. Mitrophanov, “Estimates of stability for finite homogeneous continuous-time Markov chains”, Theory Probab. Appl., 50:2 (2006), 319–326  crossref  isi
  83. A. Yu. Mitrophanov, “Sensitivity and convergence of uniformly ergodic Markov chains”, Journal of Applied Probability, 42:4 (2005), 1003  crossref
  84. Hans R. Künsch, “Recursive Monte Carlo filters: Algorithms and theoretical analysis”, Ann. Statist., 33:5 (2005)  crossref
  85. U. Narayan Bhat, Encyclopedia of Statistical Sciences, 2005  crossref
  86. A. Yu. Mitrophanov, “Sensitivity and convergence of uniformly ergodic Markov chains”, J. Appl. Probab., 42:04 (2005), 1003  crossref
  87. U. Narayan Bhat, Encyclopedia of Statistical Sciences, 2004  crossref
  88. Nicolas Chopin, “Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference”, Ann. Statist., 32:6 (2004)  crossref
  89. 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  crossref
  90. 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  crossref
  91. В. И. Оселедец, Д. В. Хмелёв, “Стохастические транспортные сети и устойчивость динамических систем”, Теория вероятн. и ее примен., 46:1 (2001), 147–154  mathnet  crossref  isi; V. I. Oseledets, D. V. Khmelev, “Stochastic Transportation Networks and Stability of Dynamical Systems”, Theory Probab. Appl., 46:1 (2002), 154–161  mathnet  crossref
  92. P. Del Moral, M. Kouritzin, L. Miclo, “On a Class of Discrete Generation Interacting Particle Systems”, Electron. J. Probab., 6:none (2001)  crossref
  93. J. Sunklodas, Limit Theorems of Probability Theory, 2000, 113  crossref
  94. Ian H. Domowitz, Mahmoud A. El-Gamal, “A Consistent Nonparametric Test of Ergodicity for Time Series with Applications”, SSRN Journal, 1999  crossref
  95. И. А. Ибрагимов, “Работы Р. Л. Добрушина о процессах Маркова”, УМН, 52:2(314) (1997), 5–9  mathnet  crossref  mathscinet  zmath  adsnasa; I. A. Ibragimov, “Dobrushin's works on Markov processes”, Russian Math. Surveys, 52:2 (1997), 239–243  crossref  isi
  96. Adolf Rhodius, “On the maximum of ergodicity coefficients, the Dobrushin ergodicity coefficient, and products of stochastic matrices”, Linear Algebra and its Applications, 253:1-3 (1997), 141  crossref
  97. Choon Peng Tan, “On the weak ergodicity of nonhomogeneous Markov chains”, Statistics & Probability Letters, 26:4 (1996), 293  crossref
  98. Н. А. Сидоров, “Законы больших чисел и центральная предельная теорема для последовательностей коэффициентов ротационных разложений”, Зап. научн. сем. ПОМИ, 223 (1995), 313–322  mathnet; N. A. Sidorov, “Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions”, J. Math. Sci. (New York), 87:6 (1997), 4180–4186  mathnet  crossref
  99. Laurent Miclo, “Remarques sur l'ergodicité des algorithmes de recuit simulé sur un graphe”, Stochastic Processes and their Applications, 58:2 (1995), 329  crossref
  100. Simon P. Eveson, Roger D. Nussbaum, “Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators”, Math. Proc. Camb. Phil. Soc., 117:3 (1995), 491  crossref
  101. D.J. Hartcfiel, “Cyclic markov set-chains”, Journal of Statistical Computation and Simulation, 46:3-4 (1993), 145  crossref
  102. Heikki Haario, Eero Saksman, “Simulated annealing process in general state space”, Advances in Applied Probability, 23:4 (1991), 866  crossref
  103. Shiro Ishikawa, Roger D. Nussbaum, “Some remarks on differential equations of quadratic type”, J Dyn Diff Equat, 3:3 (1991), 457  crossref
  104. Heikki Haario, Eero Saksman, “Simulated annealing process in general state space”, Adv. Appl. Probab., 23:04 (1991), 866  crossref
  105. Nina Gantert, “Laws of large numbers for the annealing algorithm”, Stochastic Processes and their Applications, 35:2 (1990), 309  crossref
  106. F.-C. Jeng, J.W. Woods, “Simulated annealing in compound Gaussian random fields (image processing)”, IEEE Trans. Inform. Theory, 36:1 (1990), 94  crossref
  107. Debasis Mitra, P. Tsoucas*, “Relaxations for the numerical solutions of some stochastic problems”, Communications in Statistics. Stochastic Models, 4:3 (1988), 387  crossref
  108. S. Anily, A. Federgruen, “Simulated annealing methods with general acceptance probabilities”, Journal of Applied Probability, 24:3 (1987), 657  crossref
  109. S. Anily, A. Federgruen, “Simulated annealing methods with general acceptance probabilities”, J. Appl. Probab., 24:03 (1987), 657  crossref
  110. R.N. Bhattacharya, S. Ramasubramanian, “Recurrence and ergodicity of diffusions”, Journal of Multivariate Analysis, 12:1 (1982), 95  crossref
  111. Dean Isaacson, “A characterization of geometric ergodicity”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 49:3 (1979), 267  crossref
  112. 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  crossref
  113. J. F. C. Kingman, “Geometrical aspects of the theory of non-homogeneous Markov chains”, Math. Proc. Camb. Phil. Soc., 77:1 (1975), 171  crossref
  114. И. В. Евстигнеев, “Положительные матричные коциклы над динамическими системами”, УМН, 29:5(179) (1974), 219–220  mathnet  mathscinet  zmath
  115. Dean Isaacson, Richard Madsen, “Positive columns for stochastic matrices”, J. Appl. Probab., 11:04 (1974), 829  crossref
  116. Dean Isaacson, Richard Madsen, “Positive columns for stochastic matrices”, Journal of Applied Probability, 11:4 (1974), 829  crossref


© МИАН, 2026