Fluctuation analysis for particle-based stochastic reaction-diffusion models
Probability
2023-10-16 v2 Mathematical Physics
Analysis of PDEs
Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.2206.10819,
title = {Fluctuation analysis for particle-based stochastic reaction-diffusion models},
author = {Max Heldman and Samuel Isaacson and Jingwei Ma and Konstantinos Spiliopoulos},
journal= {arXiv preprint arXiv:2206.10819},
year = {2023}
}