Functionals of a Wiener Process

  • Gopinath Kallianpur
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 13)

Abstract

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)
  1. (a)

    An L 2-convergent expansion in terms of Hermite functionals—Cameron-Martin

     
  2. (b)

    An L 2-convergent expansion in terms of multiple Wiener integrals—Ito

     
  3. (c)

    An Ito stochastic integral representation.

     

Keywords

Hilbert 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gopinath Kallianpur
    • 1
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA

Personalised recommendations