Large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations

TL;DR

This paper establishes large deviation principles for nonlinear filtering of McKean-Vlasov stochastic differential equations, using weak convergence methods to analyze related Zakai and Kushner-Stratonovich equations.

Contribution

It introduces a novel approach to derive large deviation principles for space-distribution dependent filtering equations in McKean-Vlasov SDEs.

Findings

Large deviation principle for the Zakai equation established

Large deviation principle for the Kushner-Stratonovich equation proved

Method based on weak convergence approach successfully applied

Abstract

In this paper, we study large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations. First of all, we establish the large deviation principle for the space-distribution dependent Zakai equation by a weak convergence approach. Then based on the obtained result and the relationship between the space-distribution dependent Zakai equation and the space-distribution dependent Kushner-Stratonovich equation, the large deviation principle for the latter is proved.