Large deviations for invariant measures of multivalued stochastic differential equations

ABSTRACT

In this paper, the problem of the large deviations for the invariant measures of the multivalued stochastic differential equations is considered. Under the assumptions of diffusion coefficient being non-Lipschitz and elliptic, we establish the large deviation principle for the invariant measures of the solutions to the multivalued stochastic differential equations. The proof is based on the work of large deviations and invariant measures for the solutions to the multivalued stochastic differential equations.

Keywords:

• Multivalued stochastic differential equation
• maximal monotone operator
• large deviation principle
• invariant measure
• non-Lipschitz

Mathematics Subject Classification:

• 60H10

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Grant Nos. 11901254, 11671408 and 11871484), and Postdoctoral Science Foundation of China (Grant No. 2020M671962 and 2021T140286).