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 ItĂ´ 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).


60H05 Stochastic integrals
60J65 Brownian motion
Full Text: DOI EuDML