Chargement en cours…
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...
| Cote: | Libro Electrónico |
|---|---|
| Auteurs principaux: | , , |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Providence, Rhode Island :
American Mathematical Society,
[2017]
|
| Collection: | Memoirs of the American Mathematical Society ;
no. 1171. |
| Sujets: | |
| Accès en ligne: | Texto completo |
| Résumé: | 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. |
|---|---|
| Description: | "Volume 247, number 1171 (fourth of 7 numbers), May 2017." Keywords:Loop soups, Markov processes, intersection local times. |
| Description matérielle: | 1 online resource (v, 78 pages) |
| Bibliographie: | Includes bibliographical references (pages 77-78). |
| ISBN: | 9781470437039 1470437031 |
| ISSN: | 0065-9266 ; |