Brazilian Journal of Probability and Statistics

Domains of operator semi-attraction of probability measures on Banach spaces

Phuc Ho Dang

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Abstract

The paper deals with operator (semi-) stability and domains of operator (semi-) attraction of probability measures on infinite dimensional Banach spaces: characterizations of operator (semi-) stability and of domains of (normal) operator (semi-) attraction are given; it is shown that the set of operator stable probability measures is a closed subset under weak topology; the domain of operator semi-attraction of a given stable probability measure coincides with its domain of operator attraction; and a probability measure is (semi-) stable iff its finite-dimensional projections are (semi-) stable.

Article information

Source
Braz. J. Probab. Stat., Volume 28, Number 4 (2014), 587-611.

Dates
First available in Project Euclid: 30 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1406741881

Digital Object Identifier
doi:10.1214/13-BJPS225

Mathematical Reviews number (MathSciNet)
MR3263066

Zentralblatt MATH identifier
1320.60012

Keywords
Infinitely divisible measures Lévy measures operator (semi-) stable measures (normal) domain of operator (semi-) attraction

Citation

Ho Dang, Phuc. Domains of operator semi-attraction of probability measures on Banach spaces. Braz. J. Probab. Stat. 28 (2014), no. 4, 587--611. doi:10.1214/13-BJPS225. https://projecteuclid.org/euclid.bjps/1406741881


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