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A New Proof of the Wiener-Hopf Factorization via Basu's Theorem

Part of: Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Brian Fralix  and
Colin Gallagher
Brian Fralix*
Affiliation:
Clemson University
Colin Gallagher*
Affiliation:
Clemson University
*
∗ Postal address: Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634, USA.
∗ Postal address: Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634, USA.
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Abstract

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We illustrate how Basu's theorem can be used to derive the spatial version of the Wiener-Hopf factorization for a specific class of piecewise-deterministic Markov processes. The classical factorization results for both random walks and Lévy processes follow immediately from our result. The approach is particularly elegant when used to establish the factorization for spectrally one-sided Lévy processes.

Keywords

Wiener-Hopf factorizationBasu's theoremWiener's Tauberian theoremLévy process

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 876 - 882
Copyright
© Applied Probability Trust 

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