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May, 1985 Relations Between the $s$-Selfdecomposable and Selfdecomposable Measures
Zbigniew J. Jurek
Ann. Probab. 13(2): 592-608 (May, 1985). DOI: 10.1214/aop/1176993012


The classes of the $s$-selfdecomposable and decomposable probability measures are related to the limit distributions of sequences of random variables deformed by some nonlinear or linear transformations respectively. Both are characterized in many different ways, among others as distributions of some random integrals. In particular we get that each selfdecomposable probability measure is $s$-selfdecomposable. This and other relations between these two classes seem to be rather unexpected.


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Zbigniew J. Jurek. "Relations Between the $s$-Selfdecomposable and Selfdecomposable Measures." Ann. Probab. 13 (2) 592 - 608, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0569.60011
MathSciNet: MR781426
Digital Object Identifier: 10.1214/aop/1176993012

Primary: 60B12
Secondary: 60H05

Keywords: $D_E\lbrack 0, \infty)$-valued random variable , $s$-selfdecomposable measure , Banach space , characteristic functional , infinitely divisible measure , random integral , selfdecomposable measure , weak convergence

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
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