Fluctuation analysis for particle-based stochastic reaction-diffusion models

Recent works have derived and proven the large-population mean-field limit for several classes of particle-based stochastic reaction-diffusion (PBSRD) models. These limits correspond to systems of partial integral-differential equations (PIDEs) that generalize standard mass-action reaction-diffusion PDE models. In this work we derive and prove the next order fluctuation corrections to such limits, which we show satisfy systems of stochastic PIDEs with Gaussian noise. Numerical examples are presented to illustrate how including the fluctuation corrections can enable the accurate estimation of higher order statistics of the underlying PBSRD model. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This study derives and proves the large-population mean-field limit for particle-based stochastic reaction-diffusion models, and provides the next order fluctuation corrections. Numerical examples demonstrate the importance of fluctuation corrections for accurate estimation of higher order statistics in the underlying model.