分形模型的平稳性分析

The Generalized Stationarity Analysis for Fractal Model

分数布朗运动模型是描述具有统计自相似随机过程现象的一种模型。本文讨论了分数布朗运动模型在正交小波变换下的性质，指出了分数布朗运动模型不稳定的原因，从而证明了分数布朗运动通过一个带通的滤波器后为一具有统计自相似性的平稳过程的一般结论。

The fractional Brownian motion is a model for the characterization of random process with statistic self-similarity. In this paper, the property of orthogonal wavelet transfonn offractional Brownian motion is analyzed and the non stationary reason for fractional Brownian motion is pointed out. The general conclusion that the output of fractional Brownian motion through abandpass filter is a generalized stationary process with statistic self-similarity is proven.