Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis

Normal view MARC view ISBD view

Intersection local times, loop soups, and permanental wick powers / Yves Le Jan, Michael B. Marcus and Jay Rosen.

Material type: TextPublisher: Providence : American Mathematical Society, 2017Description: v, 78 pages ; 26 cm.ISBN: 9781470436957 (alk. paper).DDC classification: 510
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 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.
Tags from this library: No tags from this library for this title.
Item type Current location Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata
510 Am512 (Browse shelf) Available 138213
Total holds: 0

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 $u(x,y)=u(y-x)$, 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.

There are no comments for this item.