On an explicit formula for the distribution of the supremum

M. S. Sgibnev

Statistics & Probability Letters, 1998, vol. 40, issue 4, 329-331

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.

Keywords: Random; walk; Supremum; Wiener-Hopf; factorization; Rational; function (search for similar items in EconPapers)
Date: 1998
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