Generating constrained run-and-tumble trajectories

@article{DeBruyne2021GeneratingCR,
  title={Generating constrained run-and-tumble trajectories},
  author={Benjamin De Bruyne and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
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 another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian stochastic processes such as Brownian motion, to a non-Markovian stochastic process driven by a telegraphic noise, with exponentially decaying correlations. We obtain effective space-time dependent… 
2 Citations
Generating stochastic trajectories with global dynamical constraints
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
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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