Tempered fractional Feynman-Kac equation: Theory and examples.
basic_science · Level V
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- Record sourced from PubMed, PMID 27078336.
- Also identified by DOI 10.1103/PhysRevE.93.032151.
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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.