Stochastic integration, trace and the skeleton of wiener functionals

Moshe Zakai

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Stochastic processes and financial applications Advanced Banach Space Theory Mathematical and Theoretical Analysis

Abstract

It is shown that the notion of trace induced by a given complete orthonormal system relates the Skorohod integral with a corresponding Ogawa‐type integral evaluated with respect to the same orthonormal systems. Similarly the multiple Wiener‐Ito integral is shown to be related to a multiple Ogawa‐type integral induced by a complete orthonormal system via the Hu‐Meyer formula with suitably defined multiple traces. The notion of skeleton of a Wiener functional relative to a given orthonormal system is defined and yields what seems to be a “natural” extension of Wiener functionals to the Cameron Martin space and the Wiener processes with a different scale.

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References

1988Stochastic calculus with anticipating integrands 1986Generalized stochastic integrals and the malliavin calculus 1988Generalized multiple stochastic integrals and the representation of wiener functionals 1990Stratonovich integral and trace 1989On the Relation Between the Stratonovich and Ogawa Integrals 1990Multiple Wiener-Ito integrals possessing a continuous extension

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1993Forward, backward and symmetric stochastic integration

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