| 基于小波变换的分数布朗运动参数估计 |
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| 引用本文： | 金达,李星野,闫树熙.基于小波变换的分数布朗运动参数估计[J].榆林高等专科学校学报,2008,18(6):28-30. |
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| 作者姓名： | 金达 李星野 闫树熙 |
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| 作者单位： | [1]上海理工大学管理学院,上海200093 [2]榆林学院数学与应用数学系,陕西榆林719000 |
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| 摘 要： | 为了估计分数布朗运动参数，对离散分数高斯噪声进行了Haar小波变换。根据“近似”小波系数方差和分数高斯噪声（DFGN）方差的关系，并结合平稳序列小波分解的性质，推导出一种估计算法。在仿真中，和修改的EM算法相比较，算法简洁，并以方均根误差和标准差为指标说明了此种方法的有效性和优越性。
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| 关 键 词： | 分数布朗运动 分形高斯噪声 haar小波变换 修改的EM算法 |
Parameter Estimation of Fractional Brownian Motion via Wavelet Transformation |
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| JIN Da,LI Xing-ye,YAN Shu-Xi.Parameter Estimation of Fractional Brownian Motion via Wavelet Transformation[J].Journal of Yulin College,2008,18(6):28-30. |
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| Authors: | JIN Da LI Xing-ye YAN Shu-Xi |
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| Institution: | JIN Da, LI Xing - ye, YAN Shu - xi ( 1. School of Management , University of Shanghai for Science and Technology, Shanghai 200093 ; 2. Department of Mathematics and Applied Mathematics, Yulin University,Yulin 719000, Shaanxi) |
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| Abstract: | In order to estimate the parameter of the fractional Brownian motion, the haar wavelet transformation is used to deal with the discrete fractal Gaussian noise （DFGN）. According to variances of wavelet approximate coefficient and fraetal Gaussian noise, combined with the theory of stable array wavelet decomposition, a method for estimating the Hurst parameter is developed. A numerical example is given to illustrate the computing accuracy of the present approach. |
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| Keywords: | fractional Brownian motion fractal Gaussian noise haar wavelet transformation modified EM computation |
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