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Brownian excursions, stochastic integrals, and representation of Wiener functionals
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Jean Picard, Labo. de Mathématiques, Université Blaise Pascal
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Abstract
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
Skorohod 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).
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Full text: PDF
Pages: 199-248
Published on: March 12, 2006
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Electronic Journal of Probability. ISSN: 1083-6489 |
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