Stationarity Detection in the Initial Transient Problem
Abstract
Let X=(X(t))(when t > or = 0) be a stochastic process with a stationary version X. It is investigated when it is possible to generate by simulation a version X-bar of X with lower initial bias than X itself, in the sense that either X-bar is stationary (has the same distribution as X) or the distribution of X-bar 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 tau plays a critical role. The negative results essentially state that without some information on this tail, no apriori 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-bar for various classes of processes with some special structure on tau, for example finite state Markov chains, Markov chains satisfying a Doeblin type minorization, and regenerative processes with tau having a bounded (p+1)th moment or having a stationary age distribution that can be generated by simulation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADA251516
Entities
People
- Hermann Thorisson
- Peter W. Glynn
- Soeren Asmussen
Organizations
- Stanford University