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  • Title: Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.
    Author: Brett T, Galla T.
    Journal: Phys Rev Lett; 2013 Jun 21; 110(25):250601. PubMed ID: 23829723.
    Abstract:
    We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
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