Intersection Local Times, Loop Soups and Permanental Wick Powers

Yves Le Jan, Michael B. Marcus, Jay Rosen (Autoren)

Buch | Softcover

78 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-3695-7 (ISBN)

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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.

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.

Introduction
Loop measures and renormalized intersection local times
Continuity of intersection local time processes
Loop soup and permanental chaos
Isomorphism Theorem I
Permanental Wick powers
Poisson chaos decomposition, I
Loop soup decomposition of permanental Wick powers
Poisson chaos decomposition, II
Convolutions of regularly varying functions
References

Erscheinungsdatum	06.07.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	160 g
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	1-4704-3695-7 / 1470436957
ISBN-13	978-1-4704-3695-7 / 9781470436957
Zustand	Neuware