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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/601| Meromorphic Lévy Processes and their Fluctuation Identities | |
| JUAN CARLOS PARDO MILLAN | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Procesos de Levy | |
| The last couple of years has seen a remarkable number of new, explicit examples of the Wiener- Hopf factorization for Levy processes where previously there had been very few. We mention in particular the many cases of spectrally negative Levy processes in [19, 33], hyper-exponential and generalized hyper-exponential Levy processes [22], Lamperti-stable processes in [8, 9, 12, 36], Hypergeometric processes in [32, 29, 10], -processes in [28] and -processes in [27]. In this paper we introduce a new family of Levy processes, which we call Meromorphic Levy processes, or just M -processes for short, which overlaps with many of the aforementioned classes. A key feature of the M -class is the identi cation of their Wiener-Hopf factors as rational functions of in nite degree written in terms of poles and roots of the Levy-Khintchin exponent, all of which appear on the imaginary axis of the complex plane. The speci c structure of the M -class Wiener- Hopf factorization enables us to explicitly handle a comprehensive suite of uctuation identities that concern rst passage problems for nite and in nite intervals for both the process itself as well as the resulting process when it is re ected in its in mum. Such identities are of fundamental interest given their repeated occurrence in various elds of applied probability such as mathematical nance, insurance risk theory and queuing theory. | |
| Centro de Investigación en Matemáticas AC | |
| 27-04-2010 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| PROCESOS DE MARKOV | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Probabilidad y Estadística |
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