Parameter estimation of discretely observed interacting particle systems

Chiara Amorino, Akram Heidari, Vytautė Pilipauskaitė and Mark Podolskij

Stochastic Processes and their Applications, 2023, vol. 163, issue C, 350-386

Abstract: 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 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 (Δn) and the number of particles ( N) satisfy Δn→0 and N→∞, and asymptotically normal when additionally the condition ΔnN→0 holds.

Keywords: Asymptotic normality; Consistency; Interacting particle systems; McKean–Vlasov equation; Nonlinear diffusion; Parameter estimation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.06.011

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