How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

Intersection Local Times, Loop Soups and Permanental Wick Powers


About this Title

Yves Le Jan, Michael B. Marcus and Jay Rosen

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 247, Number 1171
ISBNs: 978-1-4704-3695-7 (print); 978-1-4704-3703-9 (online)
DOI: https://doi.org/10.1090/memo/1171
Published electronically: January 3, 2017
Keywords:Loop soups, Markov processes, intersection local times

View full volume PDF

View other years and numbers:

Table of Contents


Chapters

  • 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

Abstract


Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -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 -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.

References [Enhancements On Off] (What's this?)