带有指数型扩散项Ornstein-Uhlenback过程的参数估计
Parameter Estimation for Fractional Ornstein-Uhlenbeck with Exponential Diffusion Term
DOI: 10.12677/SA.2019.86098, PDF,    国家自然科学基金支持
作者: 朱建慧, 闫理坦：东华大学数学系，上海
关键词: 参数估计；分数布朗运动；Parameter Estimation； Fractional Brownian Motion
摘要: 在本文中，我们研究带有指数型扩散项分数布朗运动驱动的Ornstein-Uhlenbeck过程的最小二乘估计，其中Hurst指数H≥1/2 。dXt=-θXtdt+σectdBtH，我们讨论满足相合性以及当1/2≤H≤5/8时应用多重维纳积分的中心极限定理得到-θ的渐进分布。这个最小二乘估计同时可以推导出其它类型的估计量，例如可由函数∫0TXt2dt进行表示。
Abstract: In this paper, we consider a least square estimator for the Ornstein-Uhlenbeck processes driven by fractional Brownian motion (fBm) with Hurst index H≥1/2 and exponential diffusion term. dXt=-θXtdt+σectdBtH, we prove the strong consistent of , and also obtain the asymptotic distribution of -θ, when 1/2≤H≤5/8, applying a central limit theorem for multiple Wiener integrals. This least square estimator can be used to study other estimators such as obtained by a function of ∫0TXt2dt .
文章引用：朱建慧, 闫理坦. 带有指数型扩散项Ornstein-Uhlenback过程的参数估计[J]. 统计学与应用, 2019, 8(6): 872-880. https://doi.org/10.12677/SA.2019.86098

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