Regeneration and Harris Chains

Abstract

In this chapter we introduce the important concept of regeneration, which will be used in several places in the forthcoming chapters. Intuitively speaking, a regenerative process is a general stochastic process that starts over from scratch (regenerates) at certain points. This could, e.g., be every time a recurrent Markov jump process hits a specific state or every time a reflected random walk hits zero. The exact specification of what is meant by “starting over from scratch” in terms of dependency (or independence) will be the crucial point, and just “enough” independence between the cycles will be assumed in order to secure the existence of a limiting (stationary) distribution of the process.