Reflecting image-dependent SDEs in Wasserstein space and large deviation principle

Abstract

In this article, we study a class of reflecting stochastic differential equations whose coefficients depend on image measures of solutions under a given initial measure in Wasserstein space ${\mathcal{P}}_2$. By the penalization method, the image process, which is a diffusion process in ${\mathcal{P}}_2$, is constrained in a priori given domain $\mathcal{O}\subset {\mathcal{P}}_2$. The large deviation principle for this reflecting image process is also established by weak convergence method.

Keywords:

• Wasserstein space
• large deviation
• intrinsic/lions derivative
• image-dependent SDE
• McKean–Vlasov SDE
• reflecting problem

AMS 2000 subject classifications:

• 60H15
• 60G46
• 60H10

Disclosure statement

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

Additional information

Funding

The work is supported by National Key R&D Program of China [grant number 2022YFA1006000]; National Natural Science Foundation of China [grant numbers 12071341, 11401427, 11771329, 11871052].