The Annals of Probability

Relations Between the $s$-Selfdecomposable and Selfdecomposable Measures

Zbigniew J. Jurek

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

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

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