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Brownian excursions, stochastic integrals, and representation of Wiener functionals

Authors
  • Picard, Jean
Publication Date
Jan 01, 2006
Source
HAL
Keywords
Language
English
License
Unknown
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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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