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Fluctuation analysis for particle-based stochastic reaction–diffusion models

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  • Heldman, M.
  • Isaacson, S.A.
  • Ma, J.
  • Spiliopoulos, K.

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.

Suggested Citation

  • Heldman, M. & Isaacson, S.A. & Ma, J. & Spiliopoulos, K., 2024. "Fluctuation analysis for particle-based stochastic reaction–diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923002065
    DOI: 10.1016/j.spa.2023.104234
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    References listed on IDEAS

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    1. Fernandez, Begoña & Méléard, Sylvie, 1997. "A Hilbertian approach for fluctuations on the McKean-Vlasov model," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 33-53, October.
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