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On an explicit formula for the distribution of the supremum

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  • Sgibnev, M. S.

Abstract

Let M[infinity] be the supremum of a random walk drifting to -[infinity] which is generated by the partial sums of a sequence of independent identically distributed random variables with a common distribution F. We prove that the moment generating function E exp(sM[infinity]) is a rational function if and only if the function [integral operator]0[infinity] exp(sx)F(dx) is rational.

Suggested Citation

  • Sgibnev, M. S., 1998. "On an explicit formula for the distribution of the supremum," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 329-331, November.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:4:p:329-331
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