| Description |
1 online resource (v, 78 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 247, number 1171 |
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Memoirs of the American Mathematical Society ; no. 1171.
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| Contents |
Chapter 1. Introduction Chapter 2. Loop measures and renormalized intersection local times Chapter 3. Continuity of intersection local time processes Chapter 4. Loop soup and permanental chaos Chapter 5. Isomorphism Theorem I Chapter 6. Permanental Wick powers Chapter 7. Poisson chaos decomposition, I Chapter 8. Loop soup decomposition of permanental Wick powers Chapter 9. Poisson chaos decomposition, II Chapter 10. Convolutions of regularly varying functions |
| Summary |
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 |
| Notes |
"Volume 247, number 1171 (fourth of 7 numbers), May 2017." |
| Bibliography |
Includes bibliographical references (pages 77-78) |
| Notes |
Keywords:Loop soups, Markov processes, intersection local times |
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Print version record |
| Subject |
Gaussian processes.
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Local times (Stochastic processes)
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Loop spaces.
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Gaussian processes
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Local times (Stochastic processes)
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Loop spaces
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| Form |
Electronic book
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| Author |
Marcus, Michael B., author.
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Rosen, Jay, 1948- author.
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American Mathematical Society, publisher
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| ISBN |
9781470437039 |
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1470437031 |
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