一种基于小波变换的多分形布朗运动合成算法

为了更有效地描述点状奇异性指数沿样本路径变化的信号,利用多分形的概念,在基于离散小波变换技术的基础上,提出了一种合成多分形布朗运动的新算法.该算法通过控制高斯白噪声的小波系数权来获得期望的信号局部正则性,而合成过程的收敛性由收敛因子保证.通过与基于Durbin-Levinson 和轮换矩阵嵌入技术算法的比较以及数字仿真试验,表明提出的算法不仅计算复杂度低,而且适用于生成非高斯的、自协方差函数事先未知的多分形过程.

Synthesis algorithm of multifractional Brownian motion with wavelet

In practice,the signals being analyzed are often very far from regular or smooth,and these irregular signals usually have many non-differentiable points,even nowhere differentiable.To describe the signal whose pointwise singularity varies along the sample path,in terms of the concept of multifractal,a new algorithm based on discrete wavelet transform for synthesis of multifractional Brownian motion was proposed.The desired local regularity of the multifractional process was obtained by controlling the weights of the wavelet expansion of the Gaussian white noise.The convergence of the synthesized process was controlled by an experimental factor.Compared with both Durbin-Levinson model and circulant matrix embedding model,this algorithm is not only time saving,but also appropriate for generating the multifractional process that is non-Gaussian and autocovariance function unknown in advance.The validity and rationality were verified by numerical experiments.