Necessary and sufficient conditions for unique solution to functional equations of Poincare type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Hu, Chin-Yuan¹  Lin, Gwo Dong^2,3 

[1] Natl Changhua Univ Educ, Dept Business Educ, Changhua 50058, Taiwan

[2] Hwa Kang Xing Ye Fdn, Social & Data Sci Res Ctr, Taipei 10659, Taiwan

[3] Acad Sinica, Inst Stat Sci, Taipei 11529, Taiwan

关键词: Distributional equation;    Poincare's functional equation;    Laplace-Stieltjes transform;    Probability generating function;    Characterization of distributions;   

DOI  :  10.1016/j.jmaa.2020.124399

来源: Elsevier

【 摘 要 】

Distributional equation is an important tool in the characterization theory because many characteristic properties of distributions can be transferred to such equations. Using a novel and natural approach, we retreat a remarkable distributional equation whose corresponding functional equation in terms of Laplace-Stieltjes transform is of the Poincare type. The necessary and sufficient conditions for the equation to have a unique distributional solution with finite variance are provided. This complements the previous results which involve at most the mean of the distributional solution. Besides, more general distributional (or functional) equations are investigated as well. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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