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
  • C. Monthus
  • Mathematics
    Journal 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,

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