基于粒子的随机反应扩散模型的平均场极限
Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
摘要：
基于粒子的随机反应扩散（PBSRD）模型是研究反应过程中噪声和扩散输运的生物系统的一种流行方法。在这项工作中，我们推导出粗粒度的确定性偏积分微分方程（PIDE）模型，提供了一个平均场近似的体积反应PBSRD模型，通常用于研究细胞过程的模型。我们制定了一个弱的测量值随机过程（MVSP）表示的体积反应性PBSRD模型，证明了一个简化的，但有代表性的系统，它是一致的，与常用的土井福克空间表示相应的向前方程。然后，我们证明了收敛的一般体积反应性模型MVSP的平均场PIDE在大人口（即热力学）的限制。
英文摘要：
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic partial integro-differential equation (PIDE) models that provide a mean field approximation to the volume reactivity PBSRD model, a model commonly used for studying cellular processes. We formulate a weak measure-valued stochastic process (MVSP) representation for the volume reactivity PBSRD model, demonstrating for a simplified but representative system that it is consistent with the commonly used Doi Fock Space representation of the corresponding forward equation. We then prove the convergence of the general volume reactivity model MVSP to the mean field PIDEs in the large-population (i.e. thermodynamic) limit.
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