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Zbl 0629.60061
Nualart, D.; Pardoux, E.
Stochastic calculus with anticipating integrands. (English)
[J] Probab. Theory Relat. Fields 78, No.4, 535-581 (1988). ISSN 0178-8051; ISSN 1432-2064/e

We study the stochastic integral defined by {\it 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.

MSC 2000:: *60H05 Stochastic integrals

Keywords: anticipating integrand; extended Itô formula; extension of Stratonovich's integral

Citations: Zbl 0333.60060

Cited in: Zbl 1062.60055 Zbl 0939.60065 Zbl 0918.60037 Zbl 0897.60058 Zbl 0956.60057 Zbl 0870.58011 Zbl 0824.60057 Zbl 0815.60048 Zbl 0811.60040 Zbl 0754.60056 Zbl 0754.60051 Zbl 0772.60042 Zbl 0745.60054 Zbl 0817.60062 Zbl 0729.60046 Zbl 0718.60051 Zbl 0717.60068 Zbl 0685.60062 Zbl 0674.60057 Zbl 0696.60054 Zbl 0662.60062 Zbl 0644.60043

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