Renewal Processes by Kosto V. Mitov & Edward Omey

Author:Kosto V. Mitov & Edward Omey
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In , we have

and it follows that

For , we have

This completes the proof of the theorem.

Remark 2.3

This theorem is the discrete time analog of Theorem 1.18.

Let us note that we derive the equations for the distributions of the lifetime processes conditioning on the last renewal event before time . As in the continuous time case these distributions are solutions of three renewal equations. We will derive one of them using the standard renewal argument.

Consider the residual lifetime . Note that . By conditioning on , we have

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