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

Nicolas Marie; Paul Raynaud de Fitte

doi:10.1080/17442508.2020.1815746

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arXiv · 2003.05800

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

Nicolas Marie·Paul Raynaud de Fitte

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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.

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Nicolas Marie, Paul Raynaud de Fitte. 2020-03-12. Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application. https://doi.org/10.1080/17442508.2020.1815746

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