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June 2016 Sparre Andersen identity and the last passage time
Jevgenijs Ivanovs
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J. Appl. Probab. 53(2): 600-605 (June 2016).

Abstract

It is shown that the celebrated result of Sparre Andersen for random walks and Lévy processes has intriguing consequences when the last time of the process in $(-\infty,0]$, say $\sigma$, is added to the picture. In the case of no positive jumps this leads to six random times, all of which have the same distribution—the uniform distribution on $[0,\sigma]$. Surprisingly, this result does not appear in the literature, even though it is based on some classical observations concerning exchangeable increments.

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Jevgenijs Ivanovs. "Sparre Andersen identity and the last passage time." J. Appl. Probab. 53 (2) 600 - 605, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1344.60047
MathSciNet: MR3514302

Subjects:
Primary: 60G51
Secondary: 60G50

Keywords: exchangeable increments , last passage , Time reversal , uniform law

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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