Statistical inference for perturbed multiscale dynamical systems

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• 作者：Siragan Gailus ; ^{siragan@math.bu.edu} ; Konstantinos Spiliopoulos ^{kspiliop@math.bu.edu}
• 关键词：Multiscale processes ; Small noise ; Parameter estimation ; Stochastic dynamical systems
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：2
• 页码：419-448
• 全文大小：663 K
• 卷排序：127

文摘

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.