Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory (Q2325371)

In a continuous time framework, stochastic differential equations (SDEs) driven by Gaussian processes with stationary increments have been introduced to model random evolution phenomena with long random dependence properties. In the main result of this paper, the existence and uniqueness of the invariant distribution is shown, and some upper bounds on the rate of convergence to equilibrium in terms of the asymptotic behavior of the covariance function of the Gaussian noise and fractional Brownian motion \( H \in (0,1/2) \) is outlined. This paper is well-organized with remarkable results.