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Item Details
| Title:
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INTERSECTION LOCAL TIMES, LOOP SOUPS AND PERMANENTAL WICK POWERS
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| By: |
Yves le Jan, Michael B. Marcus |
| Format: |
Paperback |
| List price:
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£66.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1470436957 |
| ISBN 13: |
9781470436957 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
30 May, 2017 |
| Series: |
Memoirs of the American Mathematical Society |
| Pages: |
78 |
| Description: |
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 $(\mathcal{V},d)$. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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