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Regularity conditions and the maximum likelihood estimation in dynamical systems with small fractional Brownian noise
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Taras Androshchuk
Published/Copyright:
December 1, 2006
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.
Key Words: Maximum likelihood estimation,; fractional Brownian noise,; dynamical system with small noise,; regularity,; strong consistency,; uniform asymptotical normality.
Published Online: 2006-12-01
Published in Print: 2006-12-01
Copyright 2006, Walter de Gruyter
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- Limiting distribution of random motion in a n-dimensional parallelepiped
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