Inversion of Analytic Characteristic Functions and Infinite Convolutions of Exponential and Laplace Densities

Albert Ferreiro-Castilla; Frederic Utzet

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Inversion of Analytic Characteristic Functions and Infinite Convolutions of Exponential and Laplace Densities

机译：解析特征函数的倒置和指数和拉普拉斯密度的无限卷积

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摘要

We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized Dirichlet series, which in turn is an infinite linear combination of exponential or Laplace densities. These results are applied to several examples.

机译：我们证明了整个函数的某些商是特征函数。在某些情况下，对应于该类型特征函数的概率测度具有可以表示为广义Dirichlet级数的密度，而该密度又是指数或Laplace密度的无限线性组合。这些结果适用于几个示例。

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来源
《Journal of Theoretical Probability》 |2012年第1期|p.205-230|共26页
作者
Albert Ferreiro-Castilla; Frederic Utzet;
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作者单位

Centre de Recerca Matemàtica, Apartat 50, 08193, Bellaterra (Barcelona), Spain;

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain;

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正文语种 eng
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关键词
Infinite convolutions; Characteristic function; Entire functions; 60E10; 60G50;

机译：无限卷积;特征函数;整函数;60E10;60G50;

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专利

1. Inversion of Analytic Characteristic Functions and Infinite Convolutions of Exponential and Laplace Densities [J] . Ferreiro-Castilla A., Utzet F. Journal of theoretical probability . 2012,第1期

机译：解析特征函数的倒置以及指数和拉普拉斯密度的无限卷积
2. Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww” [J] . Joachim Wuttke Algorithms . 2012,第4期

机译：扩展指数函数的Laplace-Fourier变换：解析误差界，双指数变换和开源实现“ libkww”
3. The approximation on analytic functions of infinite order represented by Laplace-Stieltjes transforms convergent in the half plane [J] . Xia Shen, Hong Yan Xu Journal of computational analysis and applications . 2019,第5期

机译：Laplace-Stieltjes代表无限顺序的分析函数的近似值在半平面中转换会聚
4. A Procedure for Laplace Transform Inversion Based on Smoothing Exponential-Polynomial Splines [C] . Rosanna Campagna, Costanza Conti, Salvatore Cuomo International conference on mumerical computations: theory and algorithms . 2020

机译：基于平滑指数多项式样条的拉普拉斯变换反转的过程
5. Approximating Convolution Integrals for Laplace and Exponential Fourier Transformations Using Simpson's Rule [D] . ?Hatcher, Marlana Gail 2020

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6. Laplace operators of infinite-dimensional Lie algebras and theta functions [O] . Victor G. Kac 1984

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7. Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities [O] . Ferreiro-Castilla, Albert, Utzet, Frederic 2010

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8. Integral Representation of the Exponentially Convex Functions of Infinitely Many Variables on Hilbert Spaces [R] . Okb El-Bab, A. S., El-Shazli, M. S. 1982

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Inversion of Analytic Characteristic Functions and Infinite Convolutions of Exponential and Laplace Densities

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