Ergodicity of infinite white $\alpha$-stable Systems with linear and bounded interactions

TL;DR

This paper establishes the existence and strong mixing properties of an infinite-dimensional stochastic system driven by white $eta$-stable noises, using perturbation methods on Ornstein-Uhlenbeck processes, contributing to the understanding of ergodicity in such systems.

Contribution

It introduces a novel approach to proving ergodicity of infinite white $eta$-stable systems with bounded linear interactions by perturbing Ornstein-Uhlenbeck processes.

Findings

Proved existence of the infinite-dimensional system.

Established strong mixing (ergodicity) of the system.

Applied perturbation techniques to Ornstein-Uhlenbeck $eta$-stable processes.

Abstract

We proved the existence of an infinite dimensional stochastic system driven by white $\alpha$-stable noises ($1<\alpha \leq 2$), and prove this system is strongly mixing. Our method is by perturbing Ornstein-Uhlenbeck $\alpha$-stable processes.