Renewal Theory

  • Arjun K. Gupta
  • Wei-Bin Zeng
  • Yanhong Wu


The renewal theory plays a key role in many applied probability areas, such as replacement policies in reliability, ruin probability in insurance mathematics, and system analysis in queueing theory. In this chapter, we shall first introduce the renewal theorem and its extensions including the key renewal theorem. Then we shall study some extended renewal processes, such as the delayed renewal process and defective renewal process. Meanwhile, we study the properties of the renewal functions under some special underlying distribution function classes.


Renewal Process Residual Life Interarrival Time Renewal Theory Renewal Equation 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  3. 3.Department of MathematicsCalifornia State University StanislausTurlockUSA

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