Dyadic approximation of double integrals with respect to symmetric stable processes

Terry R. McConnell, Murad S. Taqqu

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Recently, Rosinski and Woyczynski have given necessary and sufficient conditions for the existence of the double integral with respect to a symmetric stable process of index α in [1, 2). In their approach the double integral is defined as an iterated Itô-type integral. We show here that it can also be defined as the limit of integrals of step functions and that the two approaches are equivalent. For many purposes this result reduces the study of double integrals to that of quadratic forms in independent stable random variables.

Original languageEnglish (US)
Pages (from-to)323-331
Number of pages9
JournalStochastic Processes and their Applications
Volume22
Issue number2
DOIs
StatePublished - Jul 1986

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Keywords

  • multiple Wiener integral
  • p-summing maps
  • radonifying maps
  • random quadratic forms
  • stochastic integration
  • symmetric stable processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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