Wasserstein Convergence of Invariant Measures for Stochastic FitzHugh-Nagumo Lattice Systems Driven by Nonlinear Noise

Abstract

This paper focuses on the convergence of invariant measures in the Wasserstein sense for stochastic FitzHugh-Nagumo lattice systems featuring one-sided dissipative nonlinearities satisfying \(f'(z)\leq \kappa <0\) in weighted spaces as the noise intensity tends to zero. By utilizing uniform estimates of solutions, we establish that the family of invariant measures of the stochastic systems converges to the invariant measure of the corresponding deterministic systems with respect to the Wasserstein metric. Additionally, we provide an estimation for this convergence rate.