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July, 1987 Double Stochastic Integrals, Random Quadratic Forms and Random Series in Orlicz Spaces
Stanislaw Kwapien, Wojbor A. Woyczynski
Ann. Probab. 15(3): 1072-1096 (July, 1987). DOI: 10.1214/aop/1176992082

Abstract

Let $X(t), t \geq 0$, be a process with independent, symmetric and stationary increments and let $(\xi_i)$ be i.i.d. symmetric real random variables. We provide a characterization of functions $f(s, t), s, t \geq 0$, such that the double integral $\int\int f(s, t) dX(s) dX(t)$ exists, a characterization of infinite matrices $(\alpha_{ij})$ such that the double series $\sum\alpha_{ij}\xi_i\xi_j$ converges a.s. and a characterization of Orlicz space $l_\psi$ valued sequences $(a_i)$ for which the series $\sum a_i\xi_i$ converges a.s. in $l_\psi$. The above three problems are closely related.

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Stanislaw Kwapien. Wojbor A. Woyczynski. "Double Stochastic Integrals, Random Quadratic Forms and Random Series in Orlicz Spaces." Ann. Probab. 15 (3) 1072 - 1096, July, 1987. https://doi.org/10.1214/aop/1176992082

Information

Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0622.60054
MathSciNet: MR893915
Digital Object Identifier: 10.1214/aop/1176992082

Subjects:
Primary: 60H05
Secondary: 60B11 , 60B12 , 60E07

Keywords: Double stochastic integral , Orlicz space , process with independent increments , random quadratic form

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • July, 1987
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