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.

中文翻译：

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具有统计应用的分数布朗运动驱动的微分方程的几乎周期和周期解

摘要

我们表明，半线性随机微分方程的唯一解具有由分数布朗运动驱动的几乎周期性系数，在与随机动力系统相关的意义上几乎是周期性的。这种类型的几乎周期性允许在几乎周期性和周期性的情况下构建漂移参数的一致估计量。