Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 127, Issue 2, Pages 419-448Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spa.2016.06.013
Keywords
Multiscale processes; Small noise; Parameter estimation; Stochastic dynamical systems
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Funding
- National Science Foundation (NSF) [DMS-1312124]
- NSF CAREER award [DMS-1550918]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1312124] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1550918] Funding Source: National Science Foundation
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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. (C) 2016 Elsevier B.V. All rights reserved.
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