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

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 de...

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2024-11, Vol.96 (7), p.1913-1927
Main Authors: Chen, Ping, Zhai, Jianliang
Format: Article
Language:English
Subjects:
Deviation
Differential equations
large derivative principle
Malliavin derivative
Mean reflected stochastic differential equation
Smoothness
weak convergence method
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Summary: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.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2024.2365216