论文标题
基于粒子的随机反应扩散模型的平均场限制
Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
论文作者
论文摘要
基于粒子的随机反应扩散（PBSRD）模型是研究涉及反应过程中噪声和扩散运输的生物系统的流行方法。在这项工作中，我们得出了粗粒的确定性局部整数方程（PIDE）模型，该模型为体积反应性PBSRD模型提供了平均字段近似，这是一种通常用于研究细胞过程的模型。我们为体积反应性PBSRD模型制定了一个弱测量值随机过程（MVSP）表示，这证明了一个简化但代表性的系统，它与相应的前向方程的常用DOI FOCK空间表示一致。然后，我们证明了一般体积反应性模型MVSP对大种群（即热力学）极限中的平均场的收敛性。
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.
