Stochastic Processes with Distributed Delays: Chemical Langevin Equation and Linear-Noise Approximation
Stochastic Processes with Distributed Delays: Chemical Langevin Equation and Linear-Noise Approximation
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DOI：
10.1103/physrevlett.110.250601
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发表时间：
2013-06-18
影响因子：
8.6
通讯作者：
Galla, Tobias
中科院分区：
文献类型：
--
作者：
Brett, Tobias;Galla, Tobias
我们发展了一个系统的方法来线性噪声近似的随机反应系统的分布时滞。与大多数现有的工作不同，我们的形式主义不依赖于主方程，而是基于一个动态生成功能描述的概率测度的动态的所有可能的路径。我们推导出一般表达式的化学朗之万方程的一类广泛的非马尔可夫系统的分布时滞。具有延迟自抑制的基因调控模型和具有延迟恢复的流行病传播模型的例子为我们的结果的适用性提供了证据。
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.