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

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{ô} 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.

6 pages, 2 figures

References in corpus (4)

• Duality and hidden symmetries in interacting particle systems
• Duality for stochastic models of transport
• Extended duality relations between birth-death processes and partial differential equations
• Duality in stochastic processes from the viewpoint of basis expansions

Cited by in corpus (3)

• Numerical methods to evaluate Koopman matrix from system equations
• Connection among stochastic Hamilton-Jacobi-Bellman equation, path-integral, and Koopman operator on nonlinear stochastic optimal control
• Statistics for stochastic differential equations and approximations of resolvent