Tempered fractional Feynman-Kac equation: Theory and examples

Xiaochao Wu, Weihua Deng, Eli Barkai

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64 Scopus citations

Abstract

Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.

Original languageEnglish
Article number032151
JournalPhysical Review E
Volume93
Issue number3
DOIs
StatePublished - 31 Mar 2016

Bibliographical note

Publisher Copyright:
© 2016 American Physical Society.

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