Multiple stochastic integrals: Projection and iteration

Bruce Hajek, Eugene Wong

Research output: Contribution to journalArticlepeer-review


Multiple stochastic integrals are defined relative to a class of sets. The classic cases of multiple Wiener integral and Ito integral (as well as its generalization by Wong-Zakai-Yor) are recovered by specializing the class of sets appropriately. Any square-integrable functional of the Wiener process has a canonical representation in terms of the integrals. Formulas are given for projecting a stochastic integral onto the space of Wiener functionals and for representing multiple stochastic integrals as iterated integrals. Applications to a change in probability measure arising in a signal detection problem are given.

Original languageEnglish (US)
Pages (from-to)349-368
Number of pages20
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Issue number3
StatePublished - Sep 1983

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • General Mathematics


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