Yves Le Jan 
Intersection Local Times, Loop Soups and Permanental Wick Powers [PDF ebook] 

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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.

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格式 PDF ● 网页 78 ● ISBN 9781470437039 ● 出版者 American Mathematical Society ● 下载 3 时 ● 货币 EUR ● ID 8057148 ● 复制保护 Adobe DRM
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