Fluctuation analysis for particle-based stochastic reaction-diffusion models

TL;DR

This paper derives and proves fluctuation corrections for particle-based stochastic reaction-diffusion models, enhancing the accuracy of higher order statistics estimation beyond mean-field limits.

Contribution

It introduces the next order fluctuation corrections to the mean-field limits, modeled as stochastic PIDEs with Gaussian noise, for PBSRD systems.

Findings

Fluctuation corrections improve estimation of higher order statistics.

Numerical examples demonstrate the accuracy of the stochastic PIDE models.

The work extends the understanding of stochastic effects in reaction-diffusion systems.

Abstract

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.