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

Albert Ferreiro-Castilla; Frederic Utzet

doi:10.1007/s10959-010-0313-8

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

Albert Ferreiro-Castilla, Frederic Utzet

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

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. © 2010 Springer Science+Business Media, LLC.

Original language	English
Pages (from-to)	205-230
Journal	Journal of Theoretical Probability
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s10959-010-0313-8
Publication status	Published - 1 Mar 2012

Keywords

Characteristic function
Entire functions
Infinite convolutions

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10.1007/s10959-010-0313-8

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AU - Utzet, Frederic

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AB - 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. © 2010 Springer Science+Business Media, LLC.

KW - Characteristic function

KW - Entire functions

KW - Infinite convolutions

U2 - 10.1007/s10959-010-0313-8

DO - 10.1007/s10959-010-0313-8

M3 - Article

SN - 0894-9840

VL - 25

SP - 205

EP - 230

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 1

ER -

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

Abstract

Keywords

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