Mean field limits of particle-based stochastic reaction-diffusion models
Isaacson, Samuel A.
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Citation (published version)Samuel A Isaacson, Jingwei Ma, Konstantinos Spiliopoulos. "Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models." https://arxiv.org/abs/2003.11868v2
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.