Conditions Under Which a Markov Chain Converges to its Steady State in Finite Time

Authors:

27 July 1988

journal article
research article
Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences

Vol. 2 (3) , 377-382
DOI:10.1017/s0269964800000917

Abstract

Analysis of the initial transient problem of Monte Carlo steady-state simulation motivates the following question for Markov chains: when does there exist a deterministic Tsuch that P{X(T) = y|(0) = x} = ®(y), where ρ is the stationary distribution of X? We show that this can essentially never happen for a continuous-time Markov chain; in discrete time, such processes are i.i.d. provided the transition matrix is diagonalizable.

Keywords

This publication has 3 references indexed in Scilit:

Markov Processes
1986
Confidence Interval Estimation Using Standardized Time Series
Operations Research, 1983
On the class of Markov chains with finite convergence time
Stochastic Processes and their Applications, 1976