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

Ping Chen; Jianliang Zhai

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arXiv · 2303.13834

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

Ping Chen·Jianliang Zhai

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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 and the Malliavin derivative. 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.

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Ping Chen, Jianliang Zhai. 2023-03-24. Large deviation principles and Malliavin derivative for mean reflected stochastic differential equations. https://arxiv.org/abs/2303.13834

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