Large deviation principles and Malliavin derivative for mean reflected stochastic differential equations

Abstract

In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short time, the Malliavin derivative and the smoothness of the density. To prove large deviation principles, a sufficient condition for the weak convergence method, which is suitable for Mckean–Vlasov stochastic differential equation, plays an important role.

Keywords:

• Mean reflected stochastic differential equation
• large derivative principle
• weak convergence method
• Malliavin derivative

2020 Mathematics Subject Classifications:

• 60H10
• 60H15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by National Key R&D Program of China (No.2022YFA1006001), National Natural Science Foundation of China (Nos. 12131019, 12371151, 11721101). Jianliang Zhai's research is also supported by the Fundamental Research Funds for the Central Universities (Nos. WK3470000031, WK0010000081).