Higher-order statistics-based estimation of moments of first passage time for Markov chains in its reverse problem

Abstract

This paper presents a statistical approach for estimating the moments by using higher-order cumulants when the additive noise is Gaussian colored noise. It is shown that the kth-order moments of the noise samples are only related to the variance of the noise and that the estimators have the properties of unbiasedness and congruence. A numerical simulation is performed for constructing a Markov chain of continuous time parameters. The results show the validity of this algorithm.