# Generating stochastic trajectories with global dynamical constraints

@article{DeBruyne2021GeneratingST, title={Generating stochastic trajectories with global dynamical constraints}, author={Benjamin De Bruyne and Satya N. Majumdar and Henri Orland and Gr{\'e}gory Schehr}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2021}, volume={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 derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that…

## 2 Citations

Microcanonical conditioning of Markov processes on time-additive observables

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

The recent study by De Bruyne et al (2021 J. Stat. Mech. 123204), concerning the conditioning of the Brownian motion and of random walks on global dynamical constraints over a finite time-window T,…

## References

SHOWING 1-10 OF 83 REFERENCES

Effective Langevin equations for constrained stochastic processes

- Mathematics
- 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…

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.

Generating constrained run-and-tumble trajectories

- Mathematics, Physics
- 2021

We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with…

Generating discrete-time constrained random walks and Lévy flights.

- MathematicsPhysical review. E
- 2021

We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to…

Rare behavior of growth processes via umbrella sampling of trajectories.

- MathematicsPhysical review. E
- 2018

A correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories is revealed, revealing key features of growth processes can be insensitive to the precise form of the rate constants used to generate them.

Statistics of the occupation time for a class of Gaussian Markov processes

- Mathematics
- 2000

We revisit the work of Dhar and Majumdar (1999 Phys. Rev. E 59 6413) on the limiting distribution of the temporal mean Mt = t-1∫0tdu sign yu, for a Gaussian Markovian process yt depending on a…

Large-deviation functions for nonlinear functionals of a Gaussian stationary Markov process.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V]=(1/T)integral(T)(0)dT'…

Local and occupation time of a particle diffusing in a random medium.

- MathematicsPhysical review letters
- 2002

Analysis of the probability distributions of the local time and the occupation time within an observation time window of size t shows that these asymptotic behaviors get drastically modified when the random part of the potential is switched on, leading to the loss of self-averaging and wide sample to sample fluctuations.

Simulating Rare Events in Dynamical Processes

- Physics
- 2011

Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are…

The Kardar-Parisi-Zhang equation and universality class

- Mathematics
- 2011

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or…