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Discretization of invariant measures for stochastic lattice dynamical systems

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  • Li, Dingshi
  • Pu, Zhe

Abstract

This paper is devoted to studying the numerical approximation for stochastic reaction–diffusion lattice dynamical systems. The existence of numerical invariant measures for stochastic models with nonlinear noise is presented, where the backward Euler–Maruyama (BEM) method is applied for time discretization. Both the infinite dimensional discrete stochastic models and the related finite dimensional truncations are considered. A classical path convergence technique is applied to establish the convergence between invariant measures of numerical approximation and stochastic reaction–diffusion lattice model. By this procedure, the invariant measure of the stochastic reaction–diffusion lattice dynamical systems can be approximated by the numerical invariant measure of a finite dimensional truncated system as the discrete step size tends to zero.

Suggested Citation

  • Li, Dingshi & Pu, Zhe, 2026. "Discretization of invariant measures for stochastic lattice dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 473-493.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:473-493
    DOI: 10.1016/j.matcom.2025.07.008
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    References listed on IDEAS

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    1. Wang, Renhai & Wang, Bixiang, 2020. "Random dynamics of p-Laplacian lattice systems driven by infinite-dimensional nonlinear noise," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7431-7462.
    2. Eberhard Zeidler, 1985. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-5020-3, December.
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