Abstract

The Malliavin calculus (also known as the stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space. It is tailored to investigate regularity properties of the law of Wiener functionals such as solutions of stochastic differential equations. This theory was initiated by Malliavin and further developed by Stroock, Bismut, Watanabe, and others. The original motivation, and the most important application of this theory, has been to provide a probabilistic proof of Hörmander’s “sum of squares” theorem.

Keywords

Stochastic Differential Equation Stochastic Calculus Stochastic Partial Differential Equation Wiener Space Malliavin Calculus 
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.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • David Nualart
    • 1
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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