Statistical aspects of the fractional stochastic calculus
Statistical aspects of the fractional stochastic calculus
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DOI：
10.1214/009053606000001541
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发表时间：
2006-09
影响因子：
4.5
通讯作者：
C. Tudor;F. Viens
中科院分区：
文献类型：
--
作者：
C. Tudor;F. Viens
应用分数布朗运动的随机积分技术和高斯正则性理论及上确界估计，研究了满足分数布朗运动驱动的随机方程的随机过程的漂移参数的极大似然估计.证明了线性和非线性方程极大似然估计的存在性和强相合性。我们还证明了一个基本的离散版本的MLE，仍然是一个强相合估计。
We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the Gaussian theory of regularity and supremum estimation to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of H\"{o}lder-regularity (any \emph{Hurst} parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We\ also prove that a basic discretized version of the MLE, is still a strongly consistent estimator.