On the Wiener–Hopf factorization for Lévy processes with bounded positive jumps
AbstractWe study the Wiener–Hopf factorization for Lévy processes with bounded positive jumps and arbitrary negative jumps. We prove that the positive Wiener–Hopf factor can be expressed as an infinite product involving solutions to the equation ψ(z)=q, where ψ is the Laplace exponent. Under additional regularity assumptions on the Lévy measure we obtain an asymptotic expression for these solutions. When the process is spectrally negative with bounded jumps, we derive a series representation for the scale function. In order to illustrate possible applications, we discuss the implementation of numerical algorithms and present the results of several numerical experiments.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 7 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Chaumont, L. & Kyprianou, A.E. & Pardo, J.C., 2009. "Some explicit identities associated with positive self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 980-1000, March.
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