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The Polynomial Chaos Method

  • Sergey V. Lototsky
  • Boris L. Rozovsky
Chapter
Part of the Universitext book series (UTX)

Abstract

Separation of variables is a powerful idea in the study of partial differential equations, and the polynomial chaos method is a particular implementation of this idea for stochastic equations. While the elementary outcome ω is typically never mentioned explicitly in the notation of random objects, it is a variable that can potentially be separated from other variables, and the objective of this chapter is to outline a systematic approach to doing just that. Along the way, it quickly becomes clear that many ideas are closely connected to another modern branch of stochastic analysis, namely, Malliavin Calculus, and we explore these connections throughout.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sergey V. Lototsky
    • 1
  • Boris L. Rozovsky
    • 2
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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