## Abstract

Let X = {X1992}_{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 τ 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 τ. 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 τ bounded or having a stationary age distribution that can be generated by simulation.

Original language | English |
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Pages (from-to) | 130-157 |

Number of pages | 28 |

Journal | ACM Transactions on Modeling and Computer Simulation (TOMACS) |

Volume | 2 |

Issue number | 2 |

DOIs | |

Publication status | Published - 4 Jan 1992 |

## Other keywords

- coupling
- initial transient
- regenerative processes
- stationary processes