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Two Applications of Reproducing Kernel Hilbert Spaces in Stochastic Analysis

  • T. Koski
  • P. Sundar
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

The importance of reproducing kernel Hilbert spaces in the study of Gaussian processes is illustrated in two concrete problems. The first deals with mutual singularity of the law of the solution of a stochastic partial differential equation and the law of the driving process. The second gives a characterization for a Gaussian process to be a semimartingale in terms of reproducing kernel Hilbert spaces. Expansion of filtrations for Gaussian processes is discussed.

Keywords

Gaussian Process Reproduce Kernel Hilbert Space Absolute Continuity Stochastic Partial Differential Equation Brownian Sheet 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • T. Koski
    • 1
  • P. Sundar
    • 2
  1. 1.Departments of Mathematics KTHSweden
  2. 2.Department of Mathematics Louisiana State University Baton RougeUSA

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