A Law of Large Numbers and Functional Central Limit Theorem for Generalized Semi-Markov Processes

The generalized semi-Markov process (GSMP) is the usual model for the underlying stochastic process of a complex discrete-event stochastic system. Strong laws of large numbers (SLLNs) and functional central limit theorems (FCLTs) give basic conditions under which such processes exhibit stable long run behavior. These limit theorems also provide approximations for cumulative-reward distributions, confidence intervals for statistical estimators, and efficiency criteria for simulation algorithms. We prove an SLLN and FCLT for finite state GSMPs under significantly weaker conditions on the moments of the clock-setting distributions than have previously been imposed. As part of our analysis, we use Lyapunov-function arguments to show that finite moments for new clock readings imply finite moments for the od-regenerative cycles of both the GSMP and its underlying general state space Markov chain.

By: Peter W. Glynn, Peter J. Haas

Published in: RJ10315 in 2003


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