Intersection Local Times, Loop Soups and Permanental Wick Powers

Released on by Yves Le Jan
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  • Intersection Local Times, Loop Soups and Permanental Wick Powers Book Detail

  • Author : Yves Le Jan
  • Release Date : 2017-04-25
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 92
  • ISBN 13 : 1470436957
  • File Size : 14,14 MB
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Intersection Local Times, Loop Soups and Permanental Wick Powers by Yves Le Jan PDF Summary

Book Description: 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.

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