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On the maximal content of a dam and logarithmic concave renewal functions

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  • Cohen, J. W.

Abstract

For the classical dam model the distribution of the supermum of the dam content between two successive downcrossings of level x>0 by the content process is studied. The result generalizes previous results for the M/G/1 queueing system. The derivation which is rather simple is based on some recent results concerning up- and downcrossings. The resulting distribution is a functional of the solution of a renewal type integral equation occurring frequently in applied probability models. It is shown that this solution is logarithmic concave and that its reciprocal is an infinitely divisible p-function, thus leading to a number of hitherto unknown properties of a certain class of renewal functions.

Suggested Citation

  • Cohen, J. W., 1978. "On the maximal content of a dam and logarithmic concave renewal functions," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 291-304, February.
    • Handle: RePEc:eee:spapps:v:6:y:1978:i:3:p:291-304
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