论文标题
多尺度随机空间基因网络的分段确定性极限
A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network
论文作者
论文摘要
我们考虑涉及化学反应和扩散的多尺度随机空间基因网络。该模型是马尔可夫人，过渡是由泊松随机时钟驱动的。我们考虑存在两个不同的空间尺度的情况：一种具有快速动态的微观尺度和一个具有缓慢动态的宏观尺度。在微观水平上，该物种丰富，并且对于大种群限制了部分微分方程（PDE）。相反，在宏观水平上，该物种并不丰富，其动态仍然受跳跃过程的控制。它导致管理快速动态的PDE包含随机更改的系数。全球弱极限是无限的尺寸连续分段确定性马尔可夫过程（PDMP）。另外，我们证明了至上规范中的融合。
We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial scales: a microscopic one with fast dynamic and a macroscopic one with slow dynamic. At the microscopic level, the species are abundant and for the large population limit a partial differential equation (PDE) is obtained. On the contrary at the macroscopic level, the species are not abundant and their dynamic remains governed by jump processes. It results that the PDE governing the fast dynamic contains coefficients which randomly change. The global weak limit is an infinite dimensional continuous piecewise deterministic Markov process (PDMP). Also, we prove convergence in the supremum norm.
