2017/11/16 by Arnaud Debussche, Debussche, Arnaud, Mac Jugal Nguepedja Nankep +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Bioinformatics and Genomic Networks #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1711.06010
openalex publication_date 2017/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotic behavior of multiscale stochastic spatial gene networks. Multiscaling takes into account the difference of abundance between molecules , and captures the dynamic of rare species at a mesoscopic level. We introduce an assumption of spatial correlations for reactions involving rare species and a new law of large numbers is obtained. According to the scales, the whole system splits into two parts with different but coupled dynamics. The high scale component converges to the usual spatial model which is the solution of a partial differential equation, whereas, the low scale component converges to the usual homogeneous model which is the solution of an ordinary differential equation. Comparisons are made in the supremum norm.