Effective Langevin equations for constrained stochastic processes [article]

Satya N. Majumdar, Henri Orland
2015 arXiv   pre-print
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
more » ... 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.
arXiv:1503.02639v2 fatcat:rmojmqjn35gnpiwwpjpv5enwku