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On the concavity of the infinitesimal renewal function

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  • Szekli, R.

Abstract

The expected time of the first passage above a level of a process with stationary independent non-negative increments is studied. It is called infinitesimal renewal function. Results analogous to Brown's (1980) concavity result on the conventional renewal function, for the infinitesimal renewal function, are proved. Some connections with Brown's (1981) conjecture and shock models are pointed out.

Suggested Citation

  • Szekli, R., 1990. "On the concavity of the infinitesimal renewal function," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 181-184, August.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:3:p:181-184
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    Cited by:

    1. Landriault, David & Li, Bin & Loke, Sooie-Hoe & Willmot, Gordon E. & Xu, Di, 2017. "A note on the convexity of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 1-6.

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