Almost periodic and periodic solutions of differential equations driven by the fractional Brownian motion with statistical application. Issue 6 (18th August 2021) - Marie, Nicolas; Raynaud De Fitte, Paul
ABSTRACT: We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a sense related to random dynamical systems. This type of almost periodicity allows for the construction of a consistent estimator of the drift parameter in the almost periodic and periodic cases.