Discretization of invariant measures for stochastic lattice dynamical systems

Dingshi Li and Zhe Pu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 473-493

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.

Keywords: Stochastic lattice systems; Numerical invariant measures; Backward Euler–Maruyama (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:473-493

DOI: 10.1016/j.matcom.2025.07.008

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