Generating stochastic trajectories with global dynamical constraints

نویسندگان

چکیده

Abstract We propose a method to exactly generate Brownian paths x c ( t ) that are constrained return the origin at some future time f , with given fixed area A f = ∫ 0 t d x c ( stretchy="false">) under their trajectory. derive an exact effective Langevin equation force accounts for constraint. In addition, we develop corresponding approach discrete-time random walks, arbitrary jump distributions including Lévy flights, which obtain distribution encodes Finally, generalise our other types of dynamical constraints such as occupation on positive axis ${T}_{f}={\int {\Theta}\left[{x}_{c}(t)\right]$?> T mathvariant="normal">Θ or generalised quadratic ${\mathcal{A}}_{f}={\int {x}_{c}^{2}(t)$?> mathvariant="script">A 2 .

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ژورنال

عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment

سال: 2021

ISSN: ['1742-5468']

DOI: https://doi.org/10.1088/1742-5468/ac3e70