The Annals of Probability

Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta_p$-Radonifying Operators

Stamatis Cambanis, Jan Rosinski, and Wojbor A. Woyczynski

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Abstract

Necessary and sufficient conditions are given for the almost sure convergence of the quadratic form $\sum \sum f_{jk}M_jM_k$ where $(M_j)$ is a sequence of i.i.d. $p$-stable random variables. A connection is established between the convergence of the quadratic form and a radonifying property of the infinite matrix operator $(f_{kj})$.

Article information

Source
Ann. Probab., Volume 13, Number 3 (1985), 885-897.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992912

Digital Object Identifier
doi:10.1214/aop/1176992912

Mathematical Reviews number (MathSciNet)
MR799426

Zentralblatt MATH identifier
0575.60018

JSTOR
links.jstor.org

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

Keywords
Stable random variables quadratic forms $\theta_p$-radonifying operators

Citation

Cambanis, Stamatis; Rosinski, Jan; Woyczynski, Wojbor A. Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta_p$-Radonifying Operators. Ann. Probab. 13 (1985), no. 3, 885--897. doi:10.1214/aop/1176992912. https://projecteuclid.org/euclid.aop/1176992912


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