✦ LIBER ✦

On an explicit formula for the distribution of the supremum

✍ Scribed by M.S. Sgibnev

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 151 KB
Volume: 40
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(98)00122-9

No coin nor oath required. For personal study only.

✦ Synopsis

Let M~ be the supremum of a random walk drifting to -oo 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 Eexp(sM~) is a rational function if and only if the function f~'~ exp(sx)F(dx) is rational.

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