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Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift

Published online by Cambridge University Press:  01 July 2016

Svante Janson
Svante Janson*
Affiliation:
Uppsala University
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Abstract

Consider the sequence of partial sums of a sequence of i.i.d. random variables with positive expectation.

We study various random quantities defined by the sequence of partial sums, e.g. the time at which the first or last crossing of a given level occurs, the value of the partial sum immediately before or after the crossing, the minimum of all partial sums. Necessary and sufficient conditions are given for the existence of moments of these quantities.

Keywords

RANDOM WALKRENEWAL THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 4 , December 1986 , pp. 865 - 879
Copyright
Copyright © Applied Probability Trust 1986 

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