Feynman - Kac Formula for Levy Processes and Semiclassical (Euclidean) Momentum Representation

N. Privault, Xiangfeng Yang, J.-C. Zambrini

2014, v.20, Issue 3, 577-600


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 Levy-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.

Keywords: Levy process,Feynman - Kac type formula,momentum representation,large deviations


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