CONVERGENCE OF STOCHASTIC GENE NETWORKS TO HYBRID PIECEWISE DETERMINISTIC PROCESSES

• 成果类型: Article
• 署名作者: Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Montpellier
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP814
• 发表日期: 2012
• 页码: 1822-1859
• 关键词: markov-processes; expression; simulation; systems; origins; noise

摘要

We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system, we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stochastic dynamics of gene network models arising in molecular biology.