Intersection local times, loop soups and permanental Wick powers. Memoirs of the American Mathematical Society; volume 247, number 1171 (fourth of 7 numbers).

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

ISBN 10: 1470436957 / ISBN 13: 9781470436957

Editore: Providence, American Mathematical Society, 2017

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Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00741 9781470436957 Sprache: Englisch Gewicht in Gramm: 150.

Codice articolo 2484579

Dati bibliografici

• Titolo: Intersection local times, loop soups and permanental Wick powers. Memoirs of the American Mathematical Society; volume 247, number 1171 (fourth of 7 numbers).
• Editore: Providence, American Mathematical Society
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 1470436957
• ISBN 13: 9781470436957
• Rilegatura: Softcover
• Peso: 150 grammi
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

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.