论文标题
由分数布朗运动驱动的慢速系统的离散时间推断
Discrete-time inference for slow-fast systems driven by fractional Brownian motion
论文作者
论文摘要
我们研究了小噪声扰动的多尺度动力学系统的统计推断，其中慢动作是由分数布朗运动驱动的。我们基于仅从慢速过程的单个时间序列的观察结果来开发模型中赫斯特指数和未知参数的向量的统计估计器。我们证明，这些估计量既一致又渐近地正常，因为扰动的振幅和时间尺度的分离参数呈零。数值模拟说明了理论结果。
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters in the model based on a single time series of observations from the slow process only. We prove that these estimators are both consistent and asymptotically normal as the amplitude of the perturbation and the time-scale separation parameter go to zero. Numerical simulations illustrate the theoretical results.
