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ON MULTIPLE DECOMPOSABILITY OF PROBABILITY MEASURES ON R

ON MULTIPLE DECOMPOSABILITY OF PROBABILITY MEASURES ON R DEMONSTRATIO MATHEMATICAVol. XXXIVNo 22001Teresa RajbaON MULTIPLE DECOMPOSABILITYOF PROBABILITY MEASURES ON RDedicated to Professor KazimierzUrbanikAbstract. We define multiple decomposable probability measures on R(see [18]) asa generalization of Loeve's ([6], [7]) c-decomposable laws (c € R). We consider multiplydecomposability sets as a generalization of Urbanik's decomposability semigroups D(P)([21]). We characterize Bunge's nested classes of C-decomposable laws ([1]) using the properties of multiply decomposability sets. We give representations of characteristic functionsof laws, whose multiply decomposability sets contain certain sets.1. IntroductionLet <p be the characteristic function of a probability measure P on thereal line R and c € R. We say ([6], [7]) that <p is c-decomposable (P isc-decomposable) if(1.1)<p{t) = ip{ct)ipc(t),t GRfor some characteristic function <pC) corresponding to a probability Pc. LetLc denote the family of all c-decomposable laws. Many authors investigatedthose classes ([1], [2], [6], [7], [8], [10], [11], [26], [27]). In this paper we studyproperties of the classes Lc and its subclasses LCli...)Cfc (cf. [18]) and theirmultiple decomposability properties.For nondegenerate and c-decomposable laws the inequality |c| < 1 issatisfied. In the sequel we consider only nondegenerate laws and the numbersc such that 0 < |c| < 1.For nondegenerate (f and 0 < |c| < 1, ip G Lc if and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON MULTIPLE DECOMPOSABILITY OF PROBABILITY MEASURES ON R

Rajba, Teresa
Demonstratio Mathematica , Volume 34 (2): 20 – Apr 1, 2001
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References (10)

Publisher
de Gruyter
Copyright
© by Teresa Rajba
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2001-0206
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIVNo 22001Teresa RajbaON MULTIPLE DECOMPOSABILITYOF PROBABILITY MEASURES ON RDedicated to Professor KazimierzUrbanikAbstract. We define multiple decomposable probability measures on R(see [18]) asa generalization of Loeve's ([6], [7]) c-decomposable laws (c € R). We consider multiplydecomposability sets as a generalization of Urbanik's decomposability semigroups D(P)([21]). We characterize Bunge's nested classes of C-decomposable laws ([1]) using the properties of multiply decomposability sets. We give representations of characteristic functionsof laws, whose multiply decomposability sets contain certain sets.1. IntroductionLet <p be the characteristic function of a probability measure P on thereal line R and c € R. We say ([6], [7]) that <p is c-decomposable (P isc-decomposable) if(1.1)<p{t) = ip{ct)ipc(t),t GRfor some characteristic function <pC) corresponding to a probability Pc. LetLc denote the family of all c-decomposable laws. Many authors investigatedthose classes ([1], [2], [6], [7], [8], [10], [11], [26], [27]). In this paper we studyproperties of the classes Lc and its subclasses LCli...)Cfc (cf. [18]) and theirmultiple decomposability properties.For nondegenerate and c-decomposable laws the inequality |c| < 1 issatisfied. In the sequel we consider only nondegenerate laws and the numbersc such that 0 < |c| < 1.For nondegenerate (f and 0 < |c| < 1, ip G Lc if and

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 2001

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