On the functional central limit theorem for first passage time of nonlinear semi-Markov reward processes

Omid Chatrabgoun, Alireza Daneshkhah, Shahid University

Research output: Contribution to journalArticle

Abstract

In this article we examine the functional central limit theorem for the first passage time of reward processes defined over a finite state space semi-Markov process. In order to apply this process for a wider range of real-world applications, the reward functions, considered in this work, are assumed to have general forms instead of the constant rates reported in the other studies. We benefit from the martingale theory and Poisson equations to prove and establish the convergence of the first passage time of reward processes to a zero mean Brownian motion. Necessary conditions to derive the results presented in this article are the existence of variances for sojourn times in each state and second order integrability of reward functions with respect to the distribution of sojourn times. We finally verify the presented methodology through a numerical illustration.
Original languageEnglish
Pages (from-to)4737-4750
Number of pages14
JournalJournal Communications in Statistics - Theory and Methods
Volume49
Issue number19
Early online date26 Apr 2019
DOIs
Publication statusE-pub ahead of print - 26 Apr 2019

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