The Annals of Probability

Relations Between the $s$-Selfdecomposable and Selfdecomposable Measures

Zbigniew J. Jurek

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Abstract

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.

Article information

Source
Ann. Probab., Volume 13, Number 2 (1985), 592-608.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993012

Digital Object Identifier
doi:10.1214/aop/1176993012

Mathematical Reviews number (MathSciNet)
MR781426

Zentralblatt MATH identifier
0569.60011

JSTOR
links.jstor.org

Subjects
Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60H05: Stochastic integrals

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

Citation

Jurek, Zbigniew J. Relations Between the $s$-Selfdecomposable and Selfdecomposable Measures. Ann. Probab. 13 (1985), no. 2, 592--608. doi:10.1214/aop/1176993012. https://projecteuclid.org/euclid.aop/1176993012


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