Stochastic lattice models driven by a fractional Brownian motion

The aim of this talk is to analyze stochastic lattice equations driven by a non-trivial multiplicative fractional Brownian motion (fBm) with Hurst parameter in (1/2,1). We will obtain the existence of a unique solution for the model, that will rely on a fixed point argument, based on nice estimates satisfied by the stochastic integral with an fBm as integrator. Further, we will focus on investigating the long time behavior of the solution, proving that when zero is a solution of the model and the initial condition belongs to a neighborhood of zero, then the corresponding solution of the lattice equation is exponentially stable with some exponential rate.