Statistical Inference for Perturbed Multiscale Dynamical Systems

2015/04/28 by Siragan Gailus, Konstantinos Spiliopoulos, Gailus, Siragan +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1504.07645

Final form of the paper will appear in Stochastic Processes and their Applications

arxiv created 2016/06/15 · arxiv updated 2016/06/16

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.

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