Asymptotic behaviors for Volterra type McKean-Vlasov stochastic integral equations with small noise

TL;DR

This paper investigates the asymptotic behaviors of Volterra type McKean-Vlasov stochastic integral equations with small noise, establishing deviation principles, a central limit theorem, and a related Volterra integral equation for the limit.

Contribution

It introduces a comprehensive analysis of asymptotic behaviors for these equations, including large and moderate deviations, and the derivation of a new Volterra integral equation involving the Lions derivative.

Findings

Established large deviation principles

Proved moderate deviation principles

Derived the central limit theorem and associated integral equation

Abstract

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles. In addition, we obtain the central limit theorem and find the Volterra integral equation satisfied by the limiting process, which involves the Lions derivative of the drift coefficient.