叠加分数布朗运动的极大似然估计

Maximum Likelihood Estimation of Superimposed Fractional Brownian Motion

本文提出了一种对叠加分数布朗运动两分量分别进行极大似然估计的算法．首先推导了重抽样情况下分数高斯噪声的小波系数方整公式，并讨论得知不同Ｈ值时方差随尺度变化存在两种截然不同的变化趋势。利用这一特点，可以对叠加的分数布朗运动的参数分别进行极大似然估计，仿真结果表明了该算法的有效性。

In this paper, an algorithm to perform the maximum likelihood estimation of the supermpoed fractional Brownian motion respectively is proposed. Firstly we derive the variance progression of the wavelet coefficients of the resampled discrete fractional Gaussian noise (DFGN), and investigate the two totally different progressions of the variance with different H. By exploiting this property the optimal parameter estimation of two superimposed fractional Brownian motion is relized, simulation results verifies the validity of this algorithm.