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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Theorems of Fubini type for iterated stochastic integrals


Authors: Marc A. Berger and Victor J. Mizel
Journal: Trans. Amer. Math. Soc. 252 (1979), 249-274
MSC: Primary 60H05; Secondary 60H20, 93E20
MathSciNet review: 534121
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Abstract: An extension of the Itô calculus which treats iterated Itô integration, as applied to a class of two-parameter processes, is introduced. This theory includes the integration of certain anticipative integrands and introduces a notion of stochastic differential for such integrands. Among the key results is a version of Fubini's theorem for iterated stochastic integrals, in which a ``correction'' term appears. Applications to stochastic integral equations and to the Itô calculus are given, and the relation of the present development to recent work of Ogawa is described.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0534121-3
PII: S 0002-9947(1979)0534121-3
Keywords: Brownian motion, stochastic integral, Volterra equation
Article copyright: © Copyright 1979 American Mathematical Society