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On Distributions of Functionals of Anomalous Diffusion Paths.

Authors :
Carmi, Shai
Turgeman, Lior
Barkai, Eli
Source :
Journal of Statistical Physics; Dec2010, Vol. 141 Issue 6, p1071-1092, 22p, 4 Graphs
Publication Year :
2010

Abstract

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrödinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Lévy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrödinger equations that recently appeared in the literature. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00224715
Volume :
141
Issue :
6
Database :
Complementary Index
Journal :
Journal of Statistical Physics
Publication Type :
Academic Journal
Accession number :
55457344
Full Text :
https://doi.org/10.1007/s10955-010-0086-6