Intersection local times, loop soups, and permanental wick powers / Yves Le Jan, Michael B. Marcus, Jay Rosen
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Memoirs of the American Mathematical Society ; volume 247, number 1171Verlag: Providence, Rhode Island : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (v, 78 pages)Schlagwörter: Andere physische Formen: 1470436957 | 9781470436957 | 1470437031. | 9781470437039. | Erscheint auch als: Kein Titel Druck-Ausgabe | Print version: Intersection local times, loop soups, and permanental wick powers DDC-Klassifikation:- 519.2/3
- QA274.4
Inhalte:
Zusammenfassung: 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 abovePPN: PPN: 897924738Package identifier: Produktsigel: ZDB-4-NLEBK
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
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