Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application

Nicolas Marie (1) , Paul Raynaud de Fitte (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Domaines: Probabilités [math.PR]

Nicolas Marie, Paul Raynaud de Fitte. Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application. Stochastics: An International Journal of Probability and Stochastic Processes, 2021, 93 (6), pp.886-906. ⟨10.1080/17442508.2020.1815746⟩. ⟨hal-02506710v2⟩