Approximation of invariant measures for random lattice reversible Selkov systems

TL;DR

This paper develops a numerical method using the backward Euler-Maruyama scheme to approximate invariant measures of complex random lattice reversible Selkov systems, ensuring convergence from finite to infinite dimensions.

Contribution

It introduces a novel approach for approximating invariant measures in nonlinear stochastic systems with random noise, demonstrating convergence of numerical schemes to true invariant measures.

Findings

Numerical invariant measures converge to true measures as time step decreases.

Finite dimensional truncations effectively approximate infinite dimensional systems.

The backward Euler-Maruyama scheme is suitable for nonlinear stochastic models.

Abstract

This paper focuses on the numerical approximation of random lattice reversible Selkov systems. It establishes the existence of numerical invariant measures for random models with nonlinear noise, using the backward Euler-Maruyama (BEM) scheme for time discretization. The study examines both infinite dimensional discrete random models and their corresponding finite dimensional truncations. A classical path convergence technique is employed to demonstrate the convergence of the invariant measures of the BEM scheme to those of the random lattice reversible Selkov systems. As the discrete time step size approaches zero, the invariant measure of the random lattice reversible Selkov systems can be approximated by the numerical invariant measure of the finite dimensional truncated systems.