Characterization of Discrete-time Fractional Brownian motion

A. Gupta, S. Joshi
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引用次数: 6

Abstract

In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time index n and it increases as the time index of the auto-covariance matrix increases. All other eigenvalues are observed to be invariant with time index n in an asymptotic sense. The eigenvectors associated with these eigenvalues also have a fixed structure and represent different frequency channels. The eigenvector associated with the time-varying eigenvalue is a low pass filter
离散时间分数布朗运动的表征
本文给出了离散时间分数布朗运动(dfBm)的表征。因为,这些过程是非平稳的;自协方差矩阵是时间的函数。观察到,一个dfBm的自协方差矩阵的特征值依赖于表征这一过程的Hurst指数。这个自协方差矩阵只有一个特征值依赖于时间指标n,并且随着自协方差矩阵时间指标的增加而增加。在渐近意义上,观察到所有其他特征值随时间指标n不变。与这些特征值相关联的特征向量也具有固定的结构并表示不同的频率通道。与时变特征值相关联的特征向量是一个低通滤波器
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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