Renewal Process

Sivaprasad Madhira and Shailaja Deshmukh ()
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Sivaprasad Madhira: Savitribai Phule Pune University
Shailaja Deshmukh: Savitribai Phule Pune University

Chapter Chapter 10 in Introduction to Stochastic Processes Using R, 2023, pp 547-581 from Springer

Abstract: Abstract A renewal process is a generalization of a Poisson process in which sojourn times in states are independent, but not necessarily exponentially distributed. The elementary properties of a renewal process including that the renewal function uniquely determines the renewal process are established in Sect. 2. In Sect. 3, we study a limit theorem concerning long-run renewal rate for the renewal process and its applications. Section 4 is devoted to the elementary renewal theorem and the key renewal theorem. In this section, a central limit theorem for a renewal process is stated and illustrated with an example. In Sect. 5, some variations of renewal processes, such as delayed renewal process, stationary renewal process, renewal reward process, and alternating renewal process are discussed in brief. The last section presents R codes used to solve the examples in the chapter.

Date: 2023
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DOI: 10.1007/978-981-99-5601-2_10

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