Large deviations for empirical measures of switching diffusion processes with small parameters

doi:10.1007/s11464-015-0486-7

Frontiers of Mathematics in China

2015, Vol. 10

Issue (4): 949-963 https://doi.org/10.1007/s11464-015-0486-7

本期目录

Large deviations for empirical measures of switching diffusion processes with small parameters

Xiaocui MA^1,²,Fubao XI^1,^*(

)

1. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
2. Department of Mathematics, Jining University, Qufu 273155, China

全文: PDF(154 KB)

Abstract：

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.

Key words： Switching diffusion process empirical measure large deviation

收稿日期: 2015-01-31 出版日期: 2015-06-05

Corresponding Author(s): Fubao XI

引用本文:

. [J]. Frontiers of Mathematics in China, 2015, 10(4): 949-963.
Xiaocui MA,Fubao XI. Large deviations for empirical measures of switching diffusion processes with small parameters. Front. Math. China, 2015, 10(4): 949-963.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-015-0486-7
https://academic.hep.com.cn/fmc/CN/Y2015/V10/I4/949

1	Bezuidenhout C. A large deviations principle for small perturbations of random evolutions of random evolution equations. Ann Probab, 1987, 15: 646-658 https://doi.org/10.1214/aop/1176992163
2	Budhiraja A, Dupuis P, Ganguly A. Moderate deviation principles for stochastic differential equations with jumps. ArXiv: 1401.7316v1
3	Budhiraja A, Dupuis P, Maroulas V. Large deviations for infinite dimensional stochastic dynamical systems. Ann Probab, 2008, 36: 1390-1420 https://doi.org/10.1214/07-AOP362
4	Dembo A, Zeitouni O. Large Deviations Techniques and Applications. San Diego: Academic Press, 1989
5	Deuschel J D, Stroock D. Large Deviations. San Diego: Academic Press, 1989
6	Dupuis P, Ellis R. A Weak Convergence Approach to the Theory of Large Deviations. New York: Wiley, 1997 https://doi.org/10.1002/9781118165904
7	Dupuis P, Liu Y F. On the large deviation rate function for the empirical measures of reversible jump Markov processes. ArXiv: 1302.6647v1
8	Eizenberg A, Freidlin M. Large deviations for Markov processes corresponding to PDE systems. Ann Probab, 1993, 21: 1015-1044 https://doi.org/10.1214/aop/1176989280
9	Freidlin M I, A.D. Wentzell A D. Random Perturbations of Dynamical Systems. New York: Springer, 1984 https://doi.org/10.1007/978-1-4684-0176-9
10	He Q, Yin G. Large deviations for multi-scale Markovian switching systems with a small diffusion. Asymptot Anal, 2014, 87: 123-145
11	Hu Y J. A unified approach to the large deviation principle for stochastic evolution equations with small perturbations. Sci China Ser A, 1997, 27: 302-310
12	Liptser R S, Pukhalskii A A. Limit theorems on large deviations for semimartingales. Stoch Stoch Rep, 1992, 38: 201-249 https://doi.org/10.1080/17442509208833757
13	Liu W. Large deviations for stochastic evolution equations with small multiplicative noise. Appl Math Optim, 2010, 61: 27-56 https://doi.org/10.1007/s00245-009-9072-2
14	Ma X C. The rate function of large deviations for a class of diffusion processes with Markovian switching. Chinese J Shandong Univ, 2010, 45: 1-4
15	Mikami T. Large deviations theorems for empirical measures in Freidlin-Wentzel exit problems. Ann Probab, 1991, 19: 58-82 https://doi.org/10.1214/aop/1176990536
16	Mo C, Luo J W. Large deviations for stochastic differential delay equations. Nonlinear Anal, 2013, 80: 202-210 https://doi.org/10.1016/j.na.2012.10.004
17	Mohammed S-E A, Zhang T S. Large deviations for stochastic systems with memory. Discrete Contin Dyn Syst Ser B, 2006, 6: 881-893 https://doi.org/10.3934/dcdsb.2006.6.881
18	Ren J, Zhang X. Freidlin-Wentzell large deviations for homeomorphism flows of non-Lipschitz SDE. Bull Sci Math, 2005, 129: 643-655 https://doi.org/10.1016/j.bulsci.2004.12.005
19	Shao J H, Xi F B. Strong ergodicity of the regime-switching diffusion processes. Stochastic Process Appl, 2013, 123: 3903-3918 https://doi.org/10.1016/j.spa.2013.06.002
20	Stroock D W, Varadhan S R S. Multidimensional Diffusion Processes. New York: Springer, 1979
21	Varadhan S R S. Asymptotic probabilities and differential equations. Comm Pure Appl Math, 1966, 19: 261-286 https://doi.org/10.1002/cpa.3160190303
22	Varadhan S R S. Large Deviations and Applications. Philadelphia: SIAM, 1984 https://doi.org/10.1137/1.9781611970241
23	Xi F B. A large deviation theorem for empirical measures of a class of stochastic processes. Chinese J Appl Probab Statist, 1998, 14: 165-172
24	Xi F B, Yin G. Almost sure stability and instability for switching-jump-diffusion systems with state-dependent switching. J Math Anal Appl, 2013, 400: 460-474 https://doi.org/10.1016/j.jmaa.2012.10.062

Viewed

Full text

Abstract

Cited

Shared

Discussed