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

摘要

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 Hos'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.