Multiple stable integrals of Banach-valued functions
type: Item
instance of: scholarly article
title: Multiple stable integrals of Banach-valued functions
zbMATH Open document ID: 0701.60051
DOI: 10.1007/BF01045162
author: Gennady Samorodnitsky
author: Murad S. Taqqu
published in: Journal of Theoretical Probability
publication date: 1990-01-01T00:00:00Z
review text: This paper is devoted to a study of the multiple stable integrals of Banach-valued functions. Let M be a symmetric \(\alpha\)-stable random measure and S be a separable Banach space of Rademacher-type \(p\geq 1\), with \(p>\alpha\). If \(f: {\mathbb{R}}^ n\to S\) is a symmetric deterministic function vanishing on the diagonals then a sufficient condition is given for the existence of \(I_ n(f)\), a multiple integral of order n with respect to M. Moreover, the tail behaviour of the distribution function of the multiple integral is computed, namely, a formula for \(P(\| I_ n(f)\| >\epsilon)\) is given. Some applications are also presented. The paper extends, to the case of Banach-valued integrands, results of the first author and \textit{J. Szulga} [Ann. Probab. 17, No.4, 1503-1520 (1989; Zbl 0689.60051)].
reviewed by: Jacek Jakubowski
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 4149282
zbMATH Keywords: probability tails
zbMATH Keywords: multiple stable integrals
zbMATH Keywords: tail behaviour
MaRDI profile type: Publication
cites work: Q3906818
cites work: Random multilinear forms
cites work: A multiple stochastic integral with respect to a strictly p-stable random measure
cites work: On a p-stable multiple integral. I, II
cites work: Double stochastic integrals, random quadratic forms and random series in Orlicz spaces
cites work: Decoupling inequalities for polynomial chaos
cites work: On stochastic integral representation of stable processes with sample paths in Banach spaces
cites work: On path properties of certain infinitely divisible processes
cites work: On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals
cites work: Some Structure Theorems for the Symmetric Stable Laws
cites work: An asymptotic evaluation of the tail of a multiple symmetric \(\alpha\)- stable integral
cites work: Q3972784
cites work: On the multiple stable integral
cites work: Q4742050
description: scientific article; zbMATH DE number 4149282