稳定分布

Then we define the stable distribution with four equivalent ways and analyze its properties carefully. To study the stable distribution, we must know how to simulate its random variables. We can learn it intuitively by watching its plot of density function.By adding an auxiliary variable in the Chapter 4, we estimate the four parameters using Gibbs sampler.

接着给出了稳定分布的四种等价定义方法，详细的分析了稳定分布的性质，提出如何利用简单随机数产生稳定分布的随机变量以便我们进行分析研究，借助稳定分布近似密度函数的图形我们对它的特征会有更加直观的认识。

The generalized central limit theorem shows that these heavy-tailed fluctuations accumulate to a stable probability distribution.

如果尾不是太厚，则方差是有限的，且我们可以找到常见的正态极限分布，即稳定分布一种特殊情况。

To solve the problem that the-spectrum estimation performance based on covariation under the-stable noise environmentbecomes obviously worse when the distribution parameter is small,a method of fractional low-order covariance spectrum estimation was proposed.

针对在分布参数值较小时稳定分布噪声下基于共变的谱估计性能较差这一问题，提出了一种分数低阶协方差谱估计方法。

School of Electronic and Information Engineering,Dalian University of Technology,Dalian,Liaoning 116024,ChinaStable processes can better model the impulsive random signals and noises in physical observation.This paper briefly describes its spectral representation,proposes a new different spectral density from power spectrum density of second order processes,thus can get a new concept of stable white noise based on covariation spectrum,and a method of identification of nonlinear PAR system based on least p-norm.

描述了稳定分布的谱表示，提出了共变谱密度的概念，得到一种基于自共变序列与共变谱的稳定分布白噪声与有色噪声的概念及其判断标准，对传统意义上的白噪声进行了广义化，依据多项式自回归系统模型，对基于稳定白噪声输入的系统输出非线性稳定有色噪声建立其非线性PAR模型，提出基于最小P范数的EIRLP算法对非线性PAR系统进行辨识。

In chapter five, let {Xt,i 1} be ρ-mixing sequences with identical distributions, which belong to domain of normal attraction with non-generational and stable distribution. With probability one, we have limsup a.s.

第五章，设｛X_n，n≥1｝是同分布ρ-混合序列，其分布属于特征指数为α(0＜α＜2)的非退化稳定分布的正则吸引场，证明了依概率1有

In chapter five, let {Xt,i 1} be ρ-mixing sequences with identical distributions, which belong to domain of normal attraction with non-generational and stable distribution. With probability one, we havelimsup a.s.

第五章，设｛X_n，n≥1｝是同分布ρ-混合序列，其分布属于特征指数为α(0＜α＜2)的非退化稳定分布的正则吸引场，证明了依概率1有

And we show that random walk model converges to the stable law of Lévy-Feller advection-dispersion equation by use of a properly scaled transition to vanish-ing space and time steps,We propose an explicit finite difference approximation for Lévy-Feller advection-dispersion equation.

第三章讨论描述服从某种稳定分布反常扩散的非对称空间分数阶对流-扩散方程——Lévy-Feller对流-扩散方程，首先利用Fourier变换和Laplace变换给出方程的基本解，然后利用Grünwald-Letnikov分数阶导数移位离散算子离散方程中的Riesz-Feller分数阶导数得到离散格式，证明此格式可以解释为离散随机游走模型，并且证明了当时间和空间步长以一定的比率同时趋于0时，所提出的离散随机游走模型收敛到Lévy-Feller对流-扩散过程的稳定分布。

By using the generalized central limit theorem, the heavy-tailed distributions (heavy-tailed Rayleigh distribution for amplitude image and heavy-tailed exponential distribution for intensity image) are obtained from the symmetric stable distributions of real and imaginary parts of echoes. Taking the heavy-tailed Rayleigh distribution as an example, the algebraic tails of heavy-tailed distributions are explained as well as the statistics of sharp peak and heavy tail.

本文使用广义中心极限定理，由雷达回波的实部和虚部的对称稳定分布，得到SAR图像的拖尾分布（幅值图像的拖尾Rayleigh分布以及强度图像的拖尾指数分布），并以拖尾Rayleigh分布为例，讨论了拖尾分布的代数拖尾特征以及尖峰厚尾的统计特性。

The main contents and results are as follows:Firstly, the basic theories of univariate stable distribution and multivariate stabledistributions are introduced.

主要研究内容如下：首先，介绍了一元稳定分布以及多元稳定分布基本理论。

In the article we at first discuss the kind of stock log-return distribution. We find that 7 kinds function can describe stock log-return form their works: Gausses of normal distribution, Levy distribution, t distribution, spike attitude distribution, random fluctuating model, ARCH-GARCH model, divide shape Brownian movement .

本文首先讨论了股票收益分布的种类，作者对前人的工作综合发现目前描述股票收益的函数大概有七种：高斯正态分布、利维稳定分布、t标度分布、尖峰态分布、随机波动率模型、ARCH—GARCH模型、分形布朗运动，我们分别对这七种函数进行了简要的介绍。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。