• Helge Holden
  • Bernt Øksendal
  • Jan Ubøe
  • Tusheng Zhang
Part of the Universitext book series (UTX)


In this chapter we develop the general framework to be used in this book. The starting point for the discussion will be the standard white noise structures and how constructions of this kind can be given a rigorous treatment. White noise analysis can be addressed in several different ways. The presentation here is to a large extent influenced by ideas and methods used by the authors. In particular, we emphasize the use of multidimensional structures, i.e., the white noise we are about to consider will in general take on values in a multidimensional space and will also be indexed by amultidimensional parameter set.


Brownian Motion White Noise Hermite Polynomial White Noise Process Stochastic Distribution 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Helge Holden
    • 1
    • 2
  • Bernt Øksendal
    • 3
  • Jan Ubøe
    • 4
  • Tusheng Zhang
    • 5
  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Center of Mathematics and Applications University of OsloOsloNorway
  3. 3.Department of MathematicsUniversity of OsloOsloNorway
  4. 4.Department of EconomicsNorwegian School of Economics and Business AdministrationBergenNorway
  5. 5.University of Manchester School of MathematicsManchesterUK

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