Effective Langevin equations for constrained stochastic processes. (30th June 2015)

• Record Type: Journal Article
• Authors: Majumdar, Satya N; Orland, Henri
• Is Part Of: Journal of statistical mechanics. (2015:Jun.)
• Publication Date: 2015-06-30
• Subjects: 4; 4/220 -- 4/037; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/06/P06039
• Languages: English
• ISSNs: 1742-5468

Abstract

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 t f . 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–Uhlenbeck 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 a constrained path joining the two minima of a double-well. Our method allows us to generate statistically independent paths and is computationally very efficient.