Description of a stochastic system by a nonadapted stochastic process

TL;DR

This paper introduces a novel approach for describing stochastic systems with variables evolving both forward and backward in time, using a perturbation expansion suited for weak coupling and differing boundary conditions.

Contribution

The paper develops a new stochastic description method based on perturbation expansion that handles forward and backward variables with different boundary conditions.

Findings

Effective for weakly coupled forward-backward systems

Applicable when initial and final conditions differ

Compared favorably to traditional transition path sampling

Abstract

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling between forward and backward variables, and is well suited for situations in which initial and final conditions are imposed on different components of the system and the coupling between those components is weak. The form of the stochastic equations in our approach is determined by requiring that they generate the same statistics obtained in a forward description of the dynamics. Numerical tests are carried out on a few simple two-degree-of-freedom systems. The merit and the difficulties of the approach are discussed and compared to more traditional strategies based on transition path sampling and simple shooting algorithms.