Local asymptotic normality for discretely observed McKean-Vlasov diffusions

TL;DR

This paper establishes the local asymptotic normality property for discretely observed McKean-Vlasov diffusions, enabling more effective statistical inference in complex mean-field stochastic models.

Contribution

It extends LAN results to McKean-Vlasov diffusions, addressing challenges from the dependence on the process distribution and implicit transition densities.

Findings

Derived stochastic expansion of the log-likelihood ratio using Malliavin calculus

Established LAN property under specific regularity conditions

Extended LAN results from particle systems to mean-field models

Abstract

We study the local asymptotic normality (LAN) property for the likelihood function associated with discretely observed $d$-dimensional McKean-Vlasov stochastic differential equations over a fixed time interval. The model involves a joint parameter in both the drift and diffusion coefficients, introducing challenges due to its dependence on the process distribution. We derive a stochastic expansion of the log-likelihood ratio using Malliavin calculus techniques and establish the LAN property under appropriate conditions. The main technical challenge arises from the implicit nature of the transition densities, which we address through integration by parts and Gaussian-type bounds. This work extends existing LAN results for interacting particle systems to the mean-field regime, contributing to statistical inference in non-linear stochastic models