# 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…

## Figures from this paper

## 35 Citations

Conditioned Langevin Dynamics enables efficient sampling of transition paths

- Computer Science, Mathematics
- 2016

A novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time under a given potential, which warrants the generation of statistically independent transition paths.

Ab initio sampling of transition paths by conditioned Langevin dynamics.

- MathematicsThe Journal of chemical physics
- 2017

A novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time period under a given potential U(x), which warrants the generation of statistically independent transition paths.

Generating stochastic trajectories with global dynamical constraints

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

We propose a method to exactly generate Brownian paths x c (t) that are constrained to return to the origin at some future time t f , with a given fixed area Af=∫0tfdtxc(t) under their trajectory. We…

Strongly constrained stochastic processes: the multi-ends Brownian bridge

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018)) established that the distribution of the first hitting times for a diffusing particle subject to hitting an absorber is…

Diffusions conditioned on occupation measures

- Mathematics
- 2015

A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary…

Large deviations conditioned on large deviations I: Markov chain and Langevin equation

- MathematicsJournal of Statistical Physics
- 2019

We present a systematic analysis of stochastic processes conditioned on an empirical observable $$Q_T$$QT defined in a time interval [0, T], for large T. We build our analysis starting with a…

Time Between the Maximum and the Minimum of a Stochastic Process.

- MathematicsPhysical review letters
- 2019

It is demonstrated that these results can be directly applied to study the position difference between the minimal and the maximal heights of a fluctuating (1+1)-dimensional Kardar-Parisi-Zhang interface on a substrate of size L, in its stationary state.

Sweetest taboo processes

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2018

Brownian dynamics play a key role in understanding the diffusive transport of micro particles in a bounded environment. In geometries containing confining walls, physical laws determine the behavior…

Distribution of the time between maximum and minimum of random walks.

- MathematicsPhysical review. E
- 2020

It is demonstrated that the distribution of τ for Brownian motion is valid for discrete-time random walks with n steps and with a finite jump variance, in the limit n→∞.

Exact and Efficient Sampling of Conditioned Walks

- Mathematics
- 2018

A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these…

## References

SHOWING 1-10 OF 40 REFERENCES

Generating transition paths by Langevin bridges.

- MathematicsThe Journal of chemical physics
- 2011

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

- Mathematics
- 1970

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

- Mathematics
- 2005

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

- Mathematics
- 1979

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

- Mathematics, Physics
- 2004

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

- Mathematics
- 2005

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

- Mathematics
- 2007

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

- Education
- 2005

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

- Mathematics
- 2007

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.

- MathematicsPhysical review letters
- 2004

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.