In this chapter, we give an overview of ordinary renewal theory on the positive half-line. We state the basic definitions and prove the important theorems on the renewal process and the renewal function. We give a detailed proof of the elementary renewal theorem and Blackwell’s theorem and we also provide some rate of convergence results. Moreover, we discuss limit theorems for the lifetime processes and give a short overview of delayed renewal processes.
KeywordsOrdinary renewal process Delayed renewal process Elementary renewal theorem Blackwell’s theorem Key renewal theorem Lifetime processes Rate of convergence Stationary renewal process
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