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July, 1986 Random Multilinear Forms
Wieslaw Krakowiak, Jerzy Szulga
Ann. Probab. 14(3): 955-973 (July, 1986). DOI: 10.1214/aop/1176992450


We study convergence of multilinear forms $\sum f(n_1,\ldots, n_k) X_{n_1} \cdots X_{n_k}$ in symmetric independent random variables. We show that the multilinear form converges if and only if its "tetrahedronal" part and "diagonal" parts of different orders converge simultaneously. For "tetrahedronal" forms a.s. and $L_0$ convergence are equivalent. Moreover, they are equivalent to $L_p$ convergence provided $(X_k)$ satisfies a Marcinkiewicz-Paley-Zygmund condition for $p \geq 2$.


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Wieslaw Krakowiak. Jerzy Szulga. "Random Multilinear Forms." Ann. Probab. 14 (3) 955 - 973, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0593.60058
MathSciNet: MR841596
Digital Object Identifier: 10.1214/aop/1176992450

Primary: 60G42
Secondary: 15A63 , 42C15 , 46A45 , 60F25 , 60G50 , 60H99

Keywords: generalized Orlicz spaces , Marcinkiewicz-Paley-Zygmund condition , random multilinear forms

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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