Renewal Theory
Sidney I. Resnick · Birkhäuser Boston eBooks · 2002
RENEWAL PROCESSES model occurrences of events happening at random times where the times between the events can be approx-imated by independent, identically distributed random variables. With such a simple description, one wonders how flexible and powerful a tool renewal processes can be. Despite the simple description, renewal theory is one of the most basic of the building blocks in applied probability. Often a complex stochastic model has one or more embedded renewal processes, and this fact lies at the heart of the analysis of such processes and is basic to the idea of regeneration, which allows a process to be decomposed into independent, identically distributed blocks of random lengths. The dissection principle for Markov chains is an example of how to decompose a process into iid blocks.