Making Birth-Death Processes from Backward Fokker-Planck Equations for Computing Expectations in Langevin Systems
Computational Physics
2020-03-20 v2 Statistical Mechanics
Abstract
A method to direct evaluation of expectations for Langevin systems (stochastic differential equations) is proposed. The method is based on a birth-death process which is derived using combinations of dummy variables and It{\^o} formula. As a pedagogical example, a double-well system and expectations for sigmoid-type functions are used. It is shown that the proposed method has some merits from computational point of view; only one time-integration for the birth-death process gives expectations for various initial conditions in the original Langevin systems. Furthermore, the same time-integration result is available for computing various center positions of the sigmoid-type functions.
Keywords
Cite
@article{arxiv.1906.00125,
title = {Making Birth-Death Processes from Backward Fokker-Planck Equations for Computing Expectations in Langevin Systems},
author = {Jun Ohkubo},
journal= {arXiv preprint arXiv:1906.00125},
year = {2020}
}
Comments
6 pages, 2 figures