Intersection Local Times, Loop Soups and Permanental Wick Powers (Memoirs of the American Mathematical Society) - Softcover

Jan, Yves Le; Marcus, Michael B.; Rosen, Jay

Softcover

ISBN 10: 1470436957 ISBN 13: 9781470436957

Publisher: American Mathematical Society, 2017

Synopsis

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.

About this title

About the Author

Yves Le Jan, Universite Paris-Sud, Orsay, France.

Michael B. Marcus, City College, CUNY, New York, NY.

Jay Rosen, College of Staten Island, CUNY, New York, NY.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2017
• Language: English
• ISBN 10: 1470436957
• ISBN 13: 9781470436957
• Binding: Paperback
• Number of pages: 78