Two-sided Taboo Limits for Markov Processes and Associated Perfect Simulation

P. W. Glynn and H. Thorisson

Stochastic Processes and their Applications, Vol.91, 1-20 (2001)

In this paper, we study the two-sided taboo limit processes that arise when a Markov chain or process is conditioned on staying in some set A for a long period of time. The taboo limit is time-homogeneous after time 0 and time-inhomogeneous before time 0. The time-reversed limit has this same qualitative structure. The precise transition structure at the taboo limit is identi ed in the context of discrete- and continuous-time Markov chains, as well as di usions. In addition, we present a perfect simulation algorithm for generating exact samples from the quasi-stationary distribution of a nite-state Markov chain.