Simulation Output Analysis for General State Space Markov Chains
P. W. Glynn and D.L. Iglehart
Proceedings of the ORSA-TIMS Special Interest Meeting on Applied Probability-Computer Science, The Interface, 71-87 (1982)
Discrete events simulations can be modeled by generalized semi-Markov processes (GSMP's). Our goal is to estimate characteristics of the stationary distribution of a GSMP. A GSMP viewed at the embedded jump points is a general state space Markov chain (GSSMC). The regenerative method for denumerable state Markov chains does not apply since a GSSMC in general does not hit a single state infinitely often. Three approaches to this problem are discussed. The first is based on a recent construction of regeneration times for GSSMC's developed by Athreya/Ney and Nummelin. This construction can also be used to increase the frequency of regeneration points for Markov chains with a denumerable state space. The second approach decomposes the GSSMC at the hitting times of a specified set. This decomposition leads to a Doeblin recurrent Markov chain and an associated central limit theorem. The third approach involves fitting multidimensional autoregressive and autoregressive- moving average models to the GSSMC using the state space approach to time series. An example to illustrate the three approaches is discussed.