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Intersection local times, loop soups, and permanental wick powers /
Several stochastic processes related to transient Lévy processes with potential densities u(x, y) = u(y − x), that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures V endowed with a metric d. Sufficient conditions are o...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
[2017]
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1171. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | Several stochastic processes related to transient Lévy processes with potential densities u(x, y) = u(y − x), that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures V endowed with a metric d. Sufficient conditions are obtained for the continuity of these processes on (V, d). The processes include n-fold self-intersection local times of transient Lévy processes and permanental chaoses, which are 'loop soup n-fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of n-th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above. |
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| Notas: | "Volume 247, number 1171 (fourth of 7 numbers), May 2017." Keywords:Loop soups, Markov processes, intersection local times. |
| Descripción Física: | 1 online resource (v, 78 pages) |
| Bibliografía: | Includes bibliographical references (pages 77-78). |
| ISBN: | 9781470437039 1470437031 |
| ISSN: | 0065-9266 ; |