Generating stochastic trajectories with global dynamical constraints

  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},
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… 
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