Multiple stochastic integrals: Projection and iteration

  • Bruce Hajek
  • Eugene Wong


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.


Stochastic Process Probability Measure Probability Theory Signal Detection Mathematical Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Bruce Hajek
    • 1
  • Eugene Wong
    • 2
  1. 1.Department of Electrical Engineering and Coordinated Science LaboratoryUniversity of Illinois at UrbanaUSA
  2. 2.Department of Electrical Engineering and Computer Sciences and the Electronics Research LaboratoryUniversity of CaliforniaBerkeleyUSA

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