Functionals of a Wiener Process
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 13)
The purpose of this chapter is to derive representations of square-integrable functionals on Wiener space. This is a topic of importance in the theory of nonlinear prediction and filtering. The three main results in the literature derive for a square-integrable functional of a Wiener process (see definition below)
An L 2-convergent expansion in terms of Hermite functionals—Cameron-Martin
An L 2-convergent expansion in terms of multiple Wiener integrals—Ito
An Ito stochastic integral representation.
KeywordsHilbert Space Tensor Product Gaussian Process Wiener Process Reproduce Kernel Hilbert Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media New York 1980