arXiv subjects

Akram Heidari

Publications and source records attributed to Akram Heidari.

3 recordsLinked to original sources

arXiv2025

Local asymptotic normality for discretely observed McKean-Vlasov diffusions

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

math.ST↗

arXiv2025

On goodness-of-fit testing for volatility in McKean-Vlasov models

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in i.i.d. McKean-Vlasov stochastic differential equations, which model large diffusion systems with distribution-dependent dynamics. Although integrated volatility estimation for classical SDEs is well established, formal model validation and goodness-of-fit testing for McKean-Vlasov systems remain largely unexplored, particularly in settings combining large particle limits with high-frequency observations. We propose a goodness-of-fit test based on discrete observations of a particle system and study its asymptotic properties in a joint regime where both the number of particles and the sampling frequency tend to infinity. We establish asymptotic normality for the relevant volatility estimators and derive a central limit theorem for the resulting test statistic. These results provide a rigorous basis for assessing volatility specifications in high-dimensional mean-field diffusion models.

stat.ME↗

arXiv2023

Parameter estimation of discretely observed interacting particle systems

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution of the process and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval $[0, T]$, we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step ($Δ_n$) and the number of particles ($N$) satisfy $Δ_n \rightarrow 0$ and $N \rightarrow \infty$, and asymptotically normal when additionally the condition $Δ_n N \rightarrow 0$ holds.

math.ST↗