Making Birth–Death Processes from Backward Fokker–Planck Equations for Computing Expectations in Langevin Systems

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 Itô formula. As a pedagogical example, a double-well system and expectations for...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2020-04, Vol.89 (4), p.44004
Main Author: Ohkubo, Jun
Format: Article
Language:English
Subjects:
Death
Differential equations
Fokker-Planck equation
Initial conditions
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Summary: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 Itô 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.
ISSN:0031-9015
1347-4073
DOI:10.7566/JPSJ.89.044004