Nicolas Privault, Xiangfeng Yang, Jean-Claude Zambrini
Published 2013-08-11Version 1
We prove a version of the Feynman-Kac formula for Levy processes and integro-differential operators, with application to the momentum representation of suitable quantum (Euclidean) systems whose Hamiltonians involve L\'{e}vy-type potentials. Large deviation techniques are used to obtain the limiting behavior of the systems as the Planck constant approaches zero. It turns out that the limiting behavior coincides with fresh aspects of the semiclassical limit of (Euclidean) quantum mechanics. Non-trivial examples of Levy processes are considered as illustrations and precise asymptotics are given for the terms in both configuration and momentum representations.
Right inverses of Levy processes: the excursion measure in the general case
On the Feynman-Kac Formula
On maxima and ladder processes for a dense class of Levy processes
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