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.
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页码：93 / 98
页数：6
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