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Meromorphic Levy processes and their fluctuation identities

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Meromorphic Levy processes and their fluctuation identities Kuznetsov, A., Kyprianou, A. E. and Pardo, J.-C. (2012) Meromorphic Levy processes and their fluctuation identities. Annals of Applied Probability, 22 (3). pp. 1101-1135. ISSN 1050- 5164 Link to official URL (if available): AAP787 Opus: University of Bath Online Publication Store This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. See for usage policies. Please scroll down to view the document. The Annals of Applied Probability 2012, Vol. 22, No. 3, 1101–1135 DOI: 10.1214/11-AAP787 © Institute of Mathematical Statistics, 2012 MEROMORPHIC LÉVY PROCESSES AND THEIR FLUCTUATION IDENTITIES BY A. KUZNETSOV, A. E. KYPRIANOU AND J. C. PARDO York University, University of Bath and CIMAT The last couple of years has seen a remarkable number of new, explicit examples of the Wiener–Hopf factorization for Lévy processes where pre- viously there had been very few. We mention, in particular, the many cases of spectrally negative Lévy processes in [Sixth Seminar on Stochastic Anal- ysis, Random Fields and Applications (2011) 119–146, Electron. J. Probab. 13 (2008) 1672–1701], hyper-exponential and generalized hyper-exponential Lévy processes [Quant. Finance 10 (2010) 629–644], Lamperti-stable pro- cesses in [J. Appl. Probab. 43 (2006) 967–983, Probab. Math. Statist. 30 (2010) 1–28, Stochastic Process. Appl. 119 (2009) 980–1000, Bull. Sci. Math. 133 (2009) 355–382], Hypergeometric processes in [Ann. Appl. Probab. 20 (2010) 522–564, Ann. Appl. Probab. 21 (2011) 2171–2190, Bernoulli 17 (2011) 34–59], β-processes in [Ann. Appl. Probab. 20 (2010) 1801–1830] and θ -processes in [J. Appl. Probab. 47 (2010) 1023–1033]. In this paper we introduce a new family of Lévy processes, which we call Meromorphic Lévy processes, or just M-processes for short, which overla

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