ABSTRACT
Usefulness of renewal processes stems principally from asymptotic properties, not only their own but also of solutions to renewal equations. This chapter focuses on functionals of renewal processes example, recurrence time processes and of interarrival time distributions example, renewal measures. It discusses some fairly specific tests concerning structural characteristics of the interarrival distribution. Tests whether a renewal process is a Poisson or Cox process are also treated; they lead to interesting characterizations. The chapter describes techniques for statistical estimation for Markov renewal processes based on complete or censored observations. A Markov renewal process describes by times of jumps and states visited the evolution of a finite-state, continuous-time process whose structure generalizes that of a Markov process. A Markov renewal process is a collection of simultaneously evolving renewal processes, representing times of entrances to various states, with a particular interdependence, and tools developed for statistical inference for renewal processes.
