产生相关非高斯随机变量的扩散过程方法

扈罗全; 朱洪波

doi:10.3724/SP.J.1146.2006.01083

产生相关非高斯随机变量的扩散过程方法

doi: 10.3724/SP.J.1146.2006.01083

基金项目:

国家自然科学基金重点项目(60432040)，国家自然科学基金项目(60572024)，教育部新世纪优秀人才支持计划(NCET-04-0519)和教育部博士点基金项目(200509230031)资助课题

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出版历程
- 收稿日期: 2006-07-20
- 修回日期: 2007-01-22
- 刊出日期: 2008-02-19

The Generation of Correlated Non-Gaussian Random Variables with Diffusion Processes

摘要

摘要: 该文研究使用扩散过程产生相关非高斯随机变量。在遍历性假设的前提下，得到由随机微分方程(SDE)描述的Markov扩散过程的平稳分布，该分布由SDE模型中的漂移系数和扩散系数决定。选择扩散系数为x的一次幂，由待求随机变量所满足的平稳分布得到漂移系数，确定所需要的SDE，并使用Milstein高阶法求解此方程得到所需的随机变量。改变扩散系数中的常数可以改变所得随机样本的相关特性。以Nakagami分布和K-分布为例进行仿真分析，验证本文提出方法的准确性和有效性。
- 无线通信;随机微分方程;随机模型;非高斯分布;扩散过程
Abstract: Random variables of non-Gaussian distribution are produced by diffusion processes. Under the assumption of ergodicity, the stationary distribution of Markov diffusion processes described by a Stochastic Differential Equation (SDE) is obtained, which is determined by drift coefficient and diffusion coefficient. Let the drift coefficient be the first order power of x, and then the diffusion coefficient can be derived as a function of diffusion coefficient and aimed probability density function. As a result, the SDE is determined, and its solution by using Milstein high order method produces the aimed random variables. The correlation of the random samples can be adjusted through changing the constant of diffusion coefficient. Taking the Nakagami distribution and K-distribution as examples, simulation results are similar to the theoretical value, which validates the effectiveness of this method.

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参考文献(1)

Rangaswamy M and Weiner D. Non-Gaussian random vectoridentification using spherically invariant random process.IEEE Trans. on AES , 1993, 29(1): 111-123.[2]Bede L and Munson D C. Generation of a random sequencegiving a jointly specified marginal distribution andautocovariance. IEEE Trans. on ASSP, 1982 , 30(6): 973-983.[3]Sondhi M M. Random processes with specified spectraldensity and first-order probability density. Bell SystemTechnical Journal, 1983, 62(3): 679-700.[4]Spurbeck M S and Scharf L L. Least squares filter design forperiodically correlated times series. IEEE Seventh SPWorkshop on Statistical Signal and Array Processing.Qubec, Canada, 1994: 267-270.[5]Kontorovitch V and Lyandres V. Stochastic differentialequations: An approach to the generation of continuous non-Gaussian processes[J].IEEE Trans, on SP.1995, 43(10):2372-2385[6]Primak S, Lyandres V, Kaufman O, and Kliger M. On thegeneration of correlated time series with a given probabilitydensity function[J].Signal Processing.1999, 72(2):61-68[7]Klebaner F. Introduction to Stochastic Calculus withApplication. London: Imperial College Press, 2001, Chap. 6.[8]张树京, 齐立心. 时间序列分析简明教程. 北京：清华大学出版社，北方交通大学出版社，2003, Chap. 2.Zhang S and Qi L. Course of Time Series[M]. Beijing:Tsinghua Univ Pr, North Jiaotong Univ. Pr., 2003, Chap. 2.[9]Kloeden P E, Platen E, and Schurz H. Numerical Solution ofSDE Through Computer Experiments. NY: Springer- Verlag,1994, Chap. 6.[10]Primak S.[J].Kontorovitch V, and Lyandres V. StochasticMethods and Their Applications to Communications:Stochastic Differential Equations Approach. NY: John Wiley Sons, Inc.2004,:-[11]Gradshteyn I S and Ryzhik I M. Table of Integrals, Series,and Products. 6th ed., Jeffrey A, Ed. NY: Academic,2000,Chap. 8.

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