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Taras Androshchuk

Regularity conditions and the maximum likelihood estimation in dynamical systems with small fractional Brownian noise

Keywords: maximum likelihood estimation, fractional Brownian noise, dynamical system with small noise, Regularity, strong consistency, uniform asymptotical normality

We give sufficient conditions under which dynamical system with small fractional Brownian noise generates a set of regular statistical experiments in a sense of Ibragimov and Has'minskii's definition. As a corollary, the maximum likelihood estimator of unknown parameter based on the observation of trajectory is consistent, uniformly asymptotically normal and its moments converge to the ones of the standard normal distribution.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 14, 12/2006
Pages: 335 - 366

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