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Stochastic calculus with anticipating integrands. (English) Zbl 0629.60061
We study the stochastic integral defined by A. V. Skorohod in Teor. Veroyatn. Primen. 20, 223-238 (1975; Zbl 0333.60060) of a possibly anticipating integrand, as a function of its upper limit, and establish an extended Itô formula. We also introduce an extension of Stratonovich’s integral, and establish the associated chain rule. In all the results, the adaptedness of the integrand is replaced by a certain smoothness requirement.

60H05 Stochastic integrals
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