title: Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.
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.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom. tobias.brett@postgrad.manchester.ac.uk
authors.forename: Tobias
authors.initials: T
authors.lastname: Brett
authors.forename: Tobias
authors.initials: T
authors.lastname: Galla
mesh_terms: D004812:Epidemiologic Methods; D005786:Gene Expression Regulation; D016014:Linear Models; D008956:Models, Chemical; D008957:Models, Genetic; D013269:Stochastic Processes