On analytic continuation of characteristic functions of probability measures

被引：1

作者：

Norvidas, Saulius ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 390卷 / 01期

关键词：

Characteristic function; Complex-valued harmonic function; Cauchy transform; Analytic function; Completely monotonic function; Absolutely monotonic function;

D O I：

10.1016/j.jmaa.2012.01.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive necessary and sufficient conditions for a continuous bounded function f :R -> C to be a characteristic function of a probability measure. The Cauchy transform K-f of f is used as analytic continuation of f to the upper and lower half-planes in C. The conditions depend on the behavior of K-f (z) and its derivatives on the imaginary axis in C. The main results are given in terms of completely monotonic and absolutely monotonic functions. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：93 / 98

页数：6

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