Maximum principle for optimal control of infinite horizon stochastic difference equations driven by fractional noises

In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noises are studied. The main difficulty comes from fractional noises on infinite horizon. Motivated by discrete-time optimal control problem driven by fractional noises and on infinite horizon, the stochastic maximum principle for discrete-time control problem driven by fractional noises in infinite horizon is proved. As an application, an optimal investment problem is solved.