Special Topic: A Comprehensive Renewal Theory for General Random Walks

This chapter extends the analysis of renewal processes initiated in Chapter 8. The renewal theorem has a rich history that culminated in a unified approach due to David Blackwell.Fn1 Among the most important ideas introduced by Blackwell in this context is the notion of ladder variables. A comprehensive treatment of this theory is presented here. Example applications include the computation of certain self-similar fractal dimensions arising in iterated function systems in this chapter, and ruin problems in insurance in special topics Chapter 26.