Mathematical systems theory

, Volume 14, Issue 1, pp 25–65 | Cite as

The Malliavin calculus and its application to second order parabolic differential equations: Part I

  • Daniel W. Stroock


The first part of this paper contains a rigorous and detailed development of the Malliavin calculus and its relation to stochastic integral equations. The second part is devoted to examples of applications of this machinery to the study of solutions to the Fokker-Planck equation, associated with diffusions. The applications given are by no means exhaustive, but instead they have been chosen to demonstrate the scope of Malliavin's ideas in the hope of stimulating further investigations into this subject.


Differential Equation Integral Equation Computational Mathematic Detailed Development Malliavin Calculus 
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Copyright information

© Springer-Verlag New York Inc 1981

Authors and Affiliations

  • Daniel W. Stroock
    • 1
  1. 1.Dept. of MathematicsUniversity of ColoradoBoulderUSA

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