Intersection local times, loop soups and permanental Wick powers /
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| Author / Creator: | Le Jan, Y. (Yves), 1952- author. |
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| Imprint: | Providence, Rhode Island : American Mathematical Society, [2017] |
| Description: | v, 78 pages ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society ; volume 247, number 1171 Memoirs of the American Mathematical Society ; no. 1171. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11036364 |
| Summary: | Several stochastic processes related to transient Levy 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 $\mathcal{{V}}$ endowed with a metric $d$. Sufficient conditions are obtained for the continuity of these processes on $(\mathcal{{V}},d)$. The processes include $n$-fold self-intersection local times of transient Levy processes and permanental chaoses, which are `loop soup $n$-fold self-intersection local times' constructed from the loop soup of the Levy 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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| Item Description: | "Volume 247, number 1171 (fourth of 7 numbers), May 2017." |
| Physical Description: | v, 78 pages ; 26 cm. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9781470436957 1470436957 |
