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Some fluctuation identities for Lévy processes with jumps of the same sign

Part of: Probability theory on algebraic and topological structures Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Xiaowen Zhou
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Postal address: Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal QC, H4B 1R6, Canada. Email address: zhou@alcor.concordia.ca
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Abstract

We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

Keywords

Fluctuation identityLaplace transformLévy process with no positive jumpsone-sided exit problemtwo-sided exit problemcompletely asymmetric stable process

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1191 - 1198
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Supported by an NSERC operating grant.

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