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

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.

arXiv comment18 pages

References in corpus (5)

• Statistical aspects of the fractional stochastic calculus
• Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients
• Nonparametric Estimation in Fractional SDE
• Nonparametric Estimation for I.I.D. Paths of Fractional SDE
• Random Almost Periodic Solutions of Random Dynamical Systems

Cited by in corpus (3)

• Nonparametric Estimation for I.I.D. Paths of Fractional SDE
• On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE
• On a Calculable Skorokhod's Integral Based Projection Estimator of the Drift Function in Fractional SDE