A multiple stochastic integral with respect to a strictly p-stable random measure
type: Item
instance of: scholarly article
title: A multiple stochastic integral with respect to a strictly p-stable random measure
zbMATH Open document ID: 0648.60064
author: Wiesław Krakowiak
author: Jerzy Szulga
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: The authors give a construction of a k-tuple stochastic integral (k\(\geq 2)\) relative to a strictly p-stable random measure for \(0<p\leq 2\). The integrands are deterministic functions with values in a Banach space E. The paper extends essentially the known results on multiple stochastic integrals relative to independently scattered random measures. The method of construction uses inequalities for random (p-stable) multilinear forms. The main idea is to use recently discovered so-called decoupling inequalities. These inequalities allow the reduction of certain basic problems of multiple stochastic integration to the study of series in independent random variables, and make it possible to reduce the non- symmetric case to the symmetric case. The richness of the space of E- valued functions for which the multiple stochastic integral exists is connected with geometric properties of the Banach space E, as e.g. E being of stable type p or E satisfying the so-called multilinear contraction principle.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 11E76
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 4058561
zbMATH Keywords: strictly p-stable random measure
zbMATH Keywords: multiple stochastic integrals
zbMATH Keywords: decoupling inequalities
zbMATH Keywords: multilinear contraction principle
reviewed by: Egbert Dettweiler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991786
OpenAlex ID: W1973619715
DOI: 10.1214/AOP/1176991786
description: scientific article; zbMATH DE number 4058561