Open Access
August, 1985 Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta_p$-Radonifying Operators
Stamatis Cambanis, Jan Rosinski, Wojbor A. Woyczynski
Ann. Probab. 13(3): 885-897 (August, 1985). DOI: 10.1214/aop/1176992912


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 $(f_{kj})$.


Download Citation

Stamatis Cambanis. Jan Rosinski. Wojbor A. Woyczynski. "Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta_p$-Radonifying Operators." Ann. Probab. 13 (3) 885 - 897, August, 1985.


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

zbMATH: 0575.60018
MathSciNet: MR799426
Digital Object Identifier: 10.1214/aop/1176992912

Primary: 60E07
Secondary: 60B12

Keywords: $\theta_p$-radonifying operators , Quadratic forms , Stable random variables

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
Back to Top