基于δ型概率密度函数序列的数值Laplace反变换新算法

doi:10.3969/j.issn.0372-2112.2013.08.004

电子学报 ›› 2013, Vol. 41 ›› Issue (8): 1474-1479.DOI: 10.3969/j.issn.0372-2112.2013.08.004

基于δ型概率密度函数序列的数值Laplace反变换新算法

余志勇¹, 郭金库¹, 路宏敏²

1. 解放军第二炮兵工程大学, 陕西西安 710025;
2. 西安电子科技大学, 陕西西安 710025

收稿日期:2012-10-09 修回日期:2013-04-28 出版日期:2013-08-25
- 通讯作者:
- 余志勇
- 作者简介:
- 郭金库 男,1980年6月出生于山东菏泽,2010年获清华大学工学博士学位.主要研究方向:信号时频分布与稀疏表示. E-mail:gjk05@mails.tsinghua.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61201120)

Numerical Inversion of Laplace Transforms Base on Sequence of δ-Type Probability Density Functions

YU Zhi-yong¹, GUO Jin-ku¹, LU Hong-min²

1. The Second Artillery Engineering University, Xi'an, Shaanxi 710025, China;
2. Xi Dian University, Xi'an, Shaanxi 710025, China

Received:2012-10-09 Revised:2013-04-28 Online:2013-08-25 Published:2013-08-25

摘要/Abstract

摘要： 利用一类属于"δ型序列"并含有指数因子exp(-st)的概率密度函数,当在大于零的实数半区间上有且只有一个对应于随机变量众数的极值点横坐标时,将随机变量连续函数的数学期望用该函数的Laplace变换表出,从而导出一种基于δ型概率密度函数序列的数值Laplace反变换(NILT)算法基本框架,并把常用的Stehfest算法和Post-Widder算法统一至该框架之下.在此基础上,选择属于"δ型序列"的Gamma分布密度函数,提出一个此类NILT算法的新成员.

关键词: 数值Laplace反变换, 广义函数, δ型序列, 概率密度函数

Abstract: An algorithm framework of the numerical inversion of Laplace transforms(NILT)based on a class of probability density function,which belongs to the sequence of δ-type functions with exponential term exp(-st)was presented.If the probability density function defined for all positive variables in the abscissa has and only has an extremum abscissa corresponding to the modal value of random variables,the expectation of a continuous function of random variables can be expressed by the Laplace transform of this function.It is shown that the traditional Stehfest's and Post-Widder's NILT algorithm are two special cases of the proposed algorithm framework.Moreover,an example using the δ-type Gamma distribution density function is given to demonstrate that the novel framework can help to develop new NILT algorithms.

Key words: numerical inversion of Laplace transforms, generalized function, sequence of δ-type functions, probability density function

中图分类号:

TN911.7

余志勇, 郭金库, 路宏敏. 基于δ型概率密度函数序列的数值Laplace反变换新算法[J]. 电子学报, 2013, 41(8): 1474-1479.

YU Zhi-yong, GUO Jin-ku, LU Hong-min. Numerical Inversion of Laplace Transforms Base on Sequence of δ-Type Probability Density Functions[J]. Acta Electronica Sinica, 2013, 41(8): 1474-1479.

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基于δ型概率密度函数序列的数值Laplace反变换新算法

Numerical Inversion of Laplace Transforms Base on Sequence of δ-Type Probability Density Functions

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