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Stationarity detection in the initial transient problem

Stationarity detection in the initial transient problem Let X = {X(t)} t ≥ 0 be a stochastic process with a stationary version X * . It is investigated when it is possible to generate by simulation a version X˜ of X with lower initial bias than X itself, in the sense that either X˜ is strictly stationary (has the same distribution as X * ) or the distribution of X˜ is close to the distribution of X * . Particular attention is given to regenerative processes and Markov processes with a finite, countable, or general state space. The results are both positive and negative, and indicate that the tail of the distribution of the cycle length । plays a critical role. The negative results essentially state that without some information on this tail, no a priori computable bias reduction is possible; in particular, this is the case for the class of all Markov processes with a countably infinite state space. On the contrary, the positive results give algorithms for simulating X˜ for various classes of processes with some special structure on । . In particular, one can generate X˜ as strictly stationary for finite state Markov chains, Markov chains satisfying a Doeblin-type minorization, and regenerative processes with the cycle length । bounded or having a stationary age distribution that can be generated by simulation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

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References (32)

Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Heuristic methods
ISSN
1049-3301
DOI
10.1145/137926.137932
Publisher site
See Article on Publisher Site

Abstract

Let X = {X(t)} t ≥ 0 be a stochastic process with a stationary version X * . It is investigated when it is possible to generate by simulation a version X˜ of X with lower initial bias than X itself, in the sense that either X˜ is strictly stationary (has the same distribution as X * ) or the distribution of X˜ is close to the distribution of X * . Particular attention is given to regenerative processes and Markov processes with a finite, countable, or general state space. The results are both positive and negative, and indicate that the tail of the distribution of the cycle length । plays a critical role. The negative results essentially state that without some information on this tail, no a priori computable bias reduction is possible; in particular, this is the case for the class of all Markov processes with a countably infinite state space. On the contrary, the positive results give algorithms for simulating X˜ for various classes of processes with some special structure on । . In particular, one can generate X˜ as strictly stationary for finite state Markov chains, Markov chains satisfying a Doeblin-type minorization, and regenerative processes with the cycle length । bounded or having a stationary age distribution that can be generated by simulation.

Journal

ACM Transactions on Modeling and Computer Simulation (TOMACS)Association for Computing Machinery

Published: Apr 1, 1992

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