On Uniform Large Deviations Principle for Multi-valued SDEs via the Viscosity Solution Approach

Citation:

Jiagang REN,Jing WU.On Uniform Large Deviations Principle for Multi-valued SDEs via the Viscosity Solution Approach[J].Chinese Annals of Mathematics B,2019,40(2):285~308
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Authors:

Jiagang REN; Jing WU

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11471340, 11671408, 11871484) and the Pearl River Nova Program of Guangzhou (No.201710010045).
Abstract: This paper deals with the uniform large deviations for multivalued stochastic differential equations (MSDEs for short) by applying a stability result of the viscosity solutions of second order Hamilton-Jacobi-Belleman equations with multivalued operators. Moreover, the large deviation principle is uniform in time and in starting point.

Keywords:

Multivalued stochastic differential equation, Large deviationprinciple, Viscosity solution, Exponential tightness, Laplace limit

Classification:

60H10, 60F10, 49L25
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