Large Deviation Principle for Neutral Type Mckean-Vlasov Stochastic Differential Equations

TL;DR

This paper establishes a large deviation principle for neutral-type McKean-Vlasov stochastic differential equations, extending existing results to include neutral terms and dependence on the segment process and its distribution.

Contribution

It introduces a large deviation principle for neutral McKean-Vlasov equations under a one-sided Lipschitz condition, extending prior work to the neutral case.

Findings

Large deviation principle proven for neutral McKean-Vlasov SDEs

Extension of large deviation results to include neutral terms

Uses extended contraction principle and exponential approximation

Abstract

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift coefficient, we establish a Freidlin-Wentzell-type large deviation principle for the solution process by using the extended contraction principle combined with an exponential approximation technique. Our results extend existing large deviation principles for McKean-Vlasov equations to the neutral case.