Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applica...
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| Tipo de recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| Idioma: | inglés |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/606 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/606 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/MSC/Procesos de Levy info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1208 info:eu-repo/classification/cti/120806 |
| Sumario: | We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained in [25] and [23]. We also derive some new results related to (i) the entrance law of the stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of the stable process re ected at its past in mum and (iii) the entrance law and the last passage time of the radial part of n-dimensional symmetric stable process. |
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