Effective Langevin equations for constrained stochastic processes
Abstract
We propose a novel stochastic method to exactly generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time . These paths are weighted with a probability given by the overdamped Langevin dynamics. We show how these paths can be exactly generated by a local stochastic differential equation. The method is illustrated on the generation of Brownian bridges, Brownian meanders, Brownian excursions and constrained Ornstein-Uehlenbeck processes. In addition, we show how to solve this equation in the case of a general force acting on the particle. As an example, we show how to generate constrained path joining the two minima of a double-well. Our method allows to generate statistically independent paths, and is computationally very efficient.
Cite
@article{arxiv.1503.02639,
title = {Effective Langevin equations for constrained stochastic processes},
author = {Satya N. Majumdar and Henri Orland},
journal= {arXiv preprint arXiv:1503.02639},
year = {2015}
}