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May, 1982 An Extension of the Stochastic Integral
Marc A. Berger, Victor J. Mizel
Ann. Probab. 10(2): 435-450 (May, 1982). DOI: 10.1214/aop/1176993868


Two related extensions of the stochastic integral are discussed. These extensions allow the integrand to anticipate the Brownian motion, and arise in the study of linear stochastic integral equations. The development is based on the homogeneous chaos expansion of the integrand. Some properties of these extended integrals, and their commutativity with the classical integrals, are derived.


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Marc A. Berger. Victor J. Mizel. "An Extension of the Stochastic Integral." Ann. Probab. 10 (2) 435 - 450, May, 1982.


Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0499.60066
MathSciNet: MR647515
Digital Object Identifier: 10.1214/aop/1176993868

Primary: 60H20
Secondary: 45D05

Keywords: Brownian motion , integral equation , multiple Wiener integral , nonanticipating , resolvent , stochastic integral

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • May, 1982
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