@book{7196c92cfcd8466283af7adb7aa5fcdb,

title = "Intersection local times, loop soups and permanental wick powers",

abstract = "Several stochastic processes related to transient L{\'e}vy 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 V endowed with a metric d. Sufficient conditions are obtained for the continuity of these processes on (V, d). The processes include n-fold self-intersection local times of transient L{\'e}vy processes and permanental chaoses, which are 'loop soup n-fold self-intersection local times' constructed from the loop soup of the L{\'e}vy 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.",

author = "{Le Jan}, Yves and Marcus, {Michael B.} and Jay Rosen",

year = "2017",

month = may,

doi = "10.1090/memo/1171",

language = "English (US)",

volume = "247",

series = "Memoirs of the American Mathematical Society",

publisher = "American Mathematical Society",

edition = "1171",

}