Malliavin introduced his analysis of functionals on the [Wiener space ][1] to obtain a probabilistic proof of the Hoermander theorem.

Hoermander theorem states that the generalized Heat equation on R^n has a smooth solution
whenever the driving function is smooth, provided that the Lie algebra of the heat operator generators span the whole of R^n at each point. Of course, analysis on Wiener spaces have many applications in other areas also. This is a reference to a [review][2] of "Stochstic analysis" by Malliavin


  [1]: http://en.wikipedia.org/wiki/Abstract_Wiener_space
  [2]: http://www.math.ucsd.edu/~bdriver/DRIVER/Papers/Drivers_Papers/A20-Malliavin-Review.pdf