Intersection local times, loop soups, and permanental wick powers / Yves Le Jan, Michael B. Marcus and Jay Rosen.
By: Le Jan, Yves [author].
Contributor(s): Marcus, Michael B [author]  Rosen, Jay [author].
Material type: TextSeries: Memoirs of the American Mathematical Society ; v 247, no 1171.Publisher: Providence : American Mathematical Society, 2017Description: v, 78 pages ; 26 cm.ISBN: 9781470436957 (alk. paper).Subject(s): Gaussian processes  Local times (Stochastic processes)  Loop spacesDDC classification: 510Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

510 Am512 (Browse shelf)  Available  138213 
Includes bibliographical references.
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.
Several stochastic processes related to transient Levy processes with potential densities $u(x,y)=u(yx)$, 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 selfintersection local times of transient Levy processes and permanental chaoses, which are `loop soup $n$fold selfintersection 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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