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 language | English |
|---|---|
| Article number | 032151 |
| Journal | Physical Review E |
| Volume | 93 |
| Issue number | 3 |
| DOIs | |
| State | Published - 31 Mar 2016 |
Bibliographical note
Publisher Copyright:© 2016 American Physical Society.
Funding
This work was supported by the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2015-77, the National Natural Science Foundation of China under Grant No. 11271173, and the Israel Science Foundation.
| Funders | Funder number |
|---|---|
| National Natural Science Foundation of China | 11271173 |
| Israel Science Foundation | |
| Fundamental Research Funds for the Central Universities | lzujbky-2015-77 |