Effective Langevin equations for constrained stochastic processes

@article{Majumdar2015EffectiveLE,
  title={Effective Langevin equations for constrained stochastic processes},
  author={Satya N. Majumdar and Henri Orland},
  journal={arXiv: Statistical Mechanics},
  year={2015}
}
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… 
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References

SHOWING 1-10 OF 40 REFERENCES
Generating transition paths by Langevin bridges.
  • H. Orland
  • Mathematics
    The Journal of chemical physics
  • 2011
TLDR
A novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time t(f) is proposed, weighted with a probability given by the overdamped Langevin dynamics.
Decomposing the Brownian path
1. Starred references are to I to and McKean [3], the terminology of which is used here. Because of the method of time substitution (Chapter 5*), results on the structure of the Brownian path
On the area under a continuous time Brownian motion till its first-passage time
The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a Fokker–Planck technique. We obtain an exact expression for the area distribution for the
A Relation between Brownian Bridge and Brownian Excursion
It is shown that Brownian excursion is equal in distribution to Brownian bridge with the origin placed at its absolute minimum. This explains why the maximum of Brownian excursion and the range of
Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly
TOPICAL REVIEW: Functionals of Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of
Brownian excursion area, Wright’s constants in graph enumeration, and other Brownian areas
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz. Brownian motion, bridge, excursion, meander and double
Brownian motion: a paradigm of soft matter and biological physics
This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in a contemporary
FAST TRACK COMMUNICATION: The first-passage area for drifted Brownian motion and the moments of the Airy distribution
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures
Exact maximal height distribution of fluctuating interfaces.
TLDR
The results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables of one dimensional system of size L with both periodic and free boundary conditions.
...
...