Almost Periodic Solutions in Distribution to Affine Stochastic Differential Equations Driven by a Fractional Brownian Motion

The few works devoted to the existence of almost periodicity solutions to stochastic differential equations driven by a fractional Brownian motion impose the following condition: the coefficient of fractional stochastic part is deterministic. In this work, without this condition, using the chaos decomposition approach and the representation of the fractional Brownian motion in terms of a standard Brownian motion. Precisely, we obtain the existence and uniqueness of almost periodic solution in distribution to affine stochastic differential equation driven by a fractional Brownian motion.