Fatalov Vadim Rolandovich

Publications in Math-Net.Ru

1. Supremum of the Euclidean norms of the multidimensional Wiener process and Brownian bridge: Sharp asymptotics of probabilities of large deviations
   
   Fundam. Prikl. Mat., 23:1 (2020),  219–257
2. Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for $L^p$-functionals
   
   Izv. RAN. Ser. Mat., 82:2 (2018),  140–171
3. Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms
   
   TMF, 195:2 (2018),  171–189
4. Brownian motion on $[0,\infty)$ with linear drift, reflected at zero: exact asymptotics for ergodic means
   
   Mat. Sb., 208:7 (2017),  109–144
5. Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional
   
   TMF, 191:3 (2017),  456–472
6. Weighted $L^p$, $p\ge2$, for a wiener process: Exact asymptoties of small deviations
   
   Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 2,  17–22
7. Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$
   
   Probl. Peredachi Inf., 50:4 (2014),  79–99
8. Ergodic means for large values of $T$ and exact asymptotics of small deviations for a multi-dimensional Wiener process
   
   Izv. RAN. Ser. Mat., 77:6 (2013),  169–206
9. The Laplace method for Gaussian measures and integrals in Banach spaces
   
   Probl. Peredachi Inf., 49:4 (2013),  64–86
10. Perturbation theory series in quantum mechanics: Phase transition and exact asymptotic forms for the expansion coefficients
    
    TMF, 174:3 (2013),  416–443
11. On the Laplace method for Gaussian measures in a Banach space
    
    Teor. Veroyatnost. i Primenen., 58:2 (2013),  325–354
12. Negative-order moments for $L^p$-functionals of Wiener processes: exact asymptotics
    
    Izv. RAN. Ser. Mat., 76:3 (2012),  203–224
13. Integral Functionals for the Exponential of the Wiener Process and the Brownian Bridge: Exact Asymptotics and Legendre Functions
    
    Mat. Zametki, 92:1 (2012),  84–105
14. Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$
    
    TMF, 173:3 (2012),  453–467
15. Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method
    
    Izv. RAN. Ser. Mat., 75:4 (2011),  189–223
16. Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure
    
    TMF, 168:2 (2011),  299–340
17. Exact asymptotics of Laplace-type Wiener integrals for $L^p$-functionals
    
    Izv. RAN. Ser. Mat., 74:1 (2010),  197–224
18. Large deviations for distributions of sums of random variables: Markov chain method
    
    Probl. Peredachi Inf., 46:2 (2010),  66–90
19. Small deviations for two classes of Gaussian stationary processes and $L^p$-functionals, $0<p\le\infty$
    
    Probl. Peredachi Inf., 46:1 (2010),  68–93
20. Exact Asymptotics of Small Deviations for a Stationary Ornstein–Uhlenbeck Process and Some Gaussian Diffusion Processes in the $L_p$-Norm, $2\le p\le\infty$
    
    Probl. Peredachi Inf., 44:2 (2008),  75–95
21. Some asymptotic formulas for the Bogoliubov Gaussian measure
    
    TMF, 157:2 (2008),  286–308
22. Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein–Uhlenbeck Processes, $p>0$
    
    Teor. Veroyatnost. i Primenen., 53:1 (2008),  72–99
23. Occupation times and exact asymptotics of small deviations of Bessel processes for $L^p$-norms with $p>0$
    
    Izv. RAN. Ser. Mat., 71:4 (2007),  69–102
24. Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas
    
    Probl. Peredachi Inf., 43:3 (2007),  75–96
25. An exact asymptotics for small deviations of a nonstationary Ornstein–Uhlenbeck process in the $L^p$-norm, $p\ge2$
    
    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, no. 4,  3–8
26. Exact Asymptotics of Large Deviations of Stationary Ornstein–Uhlenbeck Processes for $L^p$-Functional, $p>0$
    
    Probl. Peredachi Inf., 42:1 (2006),  52–71
27. The Laplace method for small deviations of Gaussian processes of Wiener type
    
    Mat. Sb., 196:4 (2005),  135–160
28. Point Asymptotics for Probabilities of Large Deviations of the $\omega^2$ Statistics in Verification of the Symmetry Hypothesis
    
    Probl. Peredachi Inf., 40:3 (2004),  33–48
29. Large deviations for Gaussian processes in Hölder norm
    
    Izv. RAN. Ser. Mat., 67:5 (2003),  207–224
30. Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields
    
    Uspekhi Mat. Nauk, 58:4(352) (2003),  89–134
31. Asymptotics of large deviations of Gaussian processes of Wiener type for $L^p$-functionals, $p>0$, and the hypergeometric function
    
    Mat. Sb., 194:3 (2003),  61–82
32. Precise Laplace-type asymptotics for moderate deviations of the distributions of sums of independent Banach-valued random elements
    
    Teor. Veroyatnost. i Primenen., 48:4 (2003),  720–744
33. Asymptotics of large deviations for Wiener random fields in $L^p$-norm, nonlinear Hammerstein equations, and high-order hyperbolic boundary-value problems
    
    Teor. Veroyatnost. i Primenen., 47:4 (2002),  710–726
34. Large deviations of the $L^p$-norm of a Wiener process with drift
    
    Mat. Zametki, 65:3 (1999),  429–436
35. The double sum method for Gaussian fields with a parameter set in $l^p$
    
    Fundam. Prikl. Mat., 2:4 (1996),  1117–1141
36. Large deviations of Gaussian measures in the spaces $l^p$ and $L^p$, $p\ge 2$
    
    Teor. Veroyatnost. i Primenen., 41:3 (1996),  682–689
37. The Laplace method for probability measures in Banach spaces
    
    Uspekhi Mat. Nauk, 50:6(306) (1995),  57–150
38. The quantization in time of sample functions of differentiable Gaussian processes
    
    Proceedings of the YSU, Physical and Mathematical Sciences, 1991, no. 1,  17–24


39. Errata to the paper in TVP, v. 58, № 2, p. 325–354
    
    Teor. Veroyatnost. i Primenen., 59:2 (2014),  413–414
40. Errata to the paper in v. 41, № 3, p. 682–689
    
    Teor. Veroyatnost. i Primenen., 51:3 (2006),  634–636