2013/02/28 by Tobias Brett, Tobias Galla · 66 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Computer science #Dynamical systems theory #Evolution and Genetic Dynamics #Formalism (music) #Gene Regulatory Network Analysis #Langevin equation #Markov process #Master equation #Mathematics #Measure (data warehouse) #Noise (video) #Physics #Quantum mechanics #Statistical physics #Stochastic differential equation #Stochastic process #cond-mat.stat-mech #q-bio.QM #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.110.250601
published in Physical Review Letters 110(25), 250601 (American Physical Society) · 21 pages, 7 figures
arxiv created 2013/05/03 · openalex publication_date 2013/06/18 · arxiv updated 2013/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.