Statistical Inference for Perturbed Multiscale Dynamical Systems

TL;DR

This paper develops a rigorous statistical inference framework for small-noise-perturbed multiscale dynamical systems, establishing the properties of a maximum likelihood estimator under broad conditions.

Contribution

It introduces a comprehensive analysis of MLE consistency, asymptotic normality, and moment convergence for complex multiscale systems with unbounded and non-periodic coefficients.

Findings

Proved MLE consistency and asymptotic normality.

Derived explicit limiting variance for the estimator.

Validated theoretical results with numerical simulations.

Abstract

We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for a parameter of interest, identifying precisely its limiting variance. We allow full dependence of coefficients on both slow and fast processes, which take values in the full Euclidean space; coefficients in the equation for the slow process need not be bounded and there is no assumption of periodic dependence. The results provide a theoretical basis for calibration of small-noise-perturbed multiscale dynamical systems. Data from numerical simulations are presented to illustrate the theory.