Invariant Measures for a Random Evolution Equation with Small Perturbations

被引：0

作者：

Xi F.B. ^{[1
]}

机构：

[1] Department of Applied Mathematics, Beijing Institute of Technology

来源：

Acta Mathematica Sinica | 2001年 / 17卷 / 4期

基金：

中国国家自然科学基金;

关键词：

Coupling; Invariant measures; Large deviations; Random evolution equation;

D O I：

10.1007/s101140100127

中图分类号：

学科分类号：

摘要：

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

引用

页码：631 / 642

页数：11

共 7 条

[1]

Bezuidenhout C., A large deviations principle for small perturbations of random evolution equations, Ann. Probab., 15, pp. 646-658, (1987)

[2]

Chen M.F., From Markov Chains to Non-Equilibrium Particle Systems, (1992)

[3]

Chen M.F., Li S.F., Coupling methods for multidimensional diffusion processes, Ann. Probab., 17, pp. 151-177, (1989)

[4]

Eizenberg A., Freidlin M.I., Large deviations for Markov processes corresponding to PDE systems, Ann. Probab., 21, pp. 1015-1044, (1993)

[5]

Freidlin M.I., Wentzell A.D., Randon Perturbations of Dynamical Systems, (1984)

[6]

Hu Y.J., A unified approach to the large deviations for small perturbations of random evolution equations, Science in China, Ser A, 27, pp. 302-310, (1997)

[7]

Sowers R., Large deviations for the invariant measures of a reaction-diffusion equation with non-Gaussian perturbations, Probab. Theory Relat. Fields, 92, pp. 393-421, (1992)

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