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Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations

Author

Listed:
  • Conrado Costa

    (Mathematical Sciences & Computer Science Building)

  • Bernardo Freitas Paulo da Costa

    (Universidade Federal do Rio de Janeiro, Centro de Tecnologia Bloco C - Av. Athos da Silveira Ramos)

  • Daniel Valesin

    (University of Groningen)

Abstract

We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained is the scaling limit of a sequence of interacting particle systems and satisfies the martingale problem corresponding to the target differential equation.

Suggested Citation

  • Conrado Costa & Bernardo Freitas Paulo da Costa & Daniel Valesin, 2023. "Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1059-1087, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01187-9
    DOI: 10.1007/s10959-022-01187-9
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