Uncertain Renewal Processes by Kai Yao

Author:Kai Yao
Language: eng
Format: epub, pdf
ISBN: 9789811393457
Publisher: Springer Singapore

Proof

Since the uncertain renewal process can only take nonnegative integer values, we have

Hence, the uncertain renewal reward process has an uncertainty distribution

Note that the event

is a polyrectangle, as the uncertain renewal process is independent of the uncertain rewards ’s, and the sequence is increasing and the sequence

is decreasing with respect to the integer k. Then it follows from Theorem 3.​4 that

According to Theorem 4.1, we have

and

Hence,

The theorem is proved.

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