Effective Langevin equations for constrained stochastic processes

Satya N. Majumdar 1 Henri Orland 2

Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2015, pp.P06039

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-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.

  • 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. IPHT – Institut de Physique Théorique – UMR CNRS 3681
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