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Brownian excursions, stochastic integrals, and representation of Wiener functionals. (English) Zbl 1112.60043
Summary: A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorokhod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener functionals; this expression is an alternative to the classical Clark-Ocone formula. Moreover, this calculus enables to construct stochastic integrals of predictable or anticipating processes (forward, backward and symmetric integrals are considered).

MSC:
 60H05 Stochastic integrals 60J65 Brownian motion
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