Fractional feynman–kac equation for anomalous diffusion functionals

Shai Carmi, Eli Barkai

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

3 Scopus citations


Functionals of the path of a Brownian particle are known to obey the celebrated Feynman–Kac equation. We develop here a fractional Feynman–Kac equation for functionals of the sub–diffusive continuous-time random walk process. Several simple examples of functionals are explicitly treated such as the occupation time, the first passage time, and the maximum of the walk. In the presence of a binding field, the fractional Feynman–Kac equation describes the route to weak ergodicity breaking.

Original languageAmerican English
Title of host publicationFractional Dynamics
Subtitle of host publicationRecent Advances
PublisherWorld Scientific Publishing Co.
Number of pages23
ISBN (Electronic)9789814340595
ISBN (Print)9814340588, 9789814340588
StatePublished - 1 Jan 2011
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.


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