J. Korean Math. Soc. 2001; 38(2): 311-319
Printed March 1, 2001
Copyright © The Korean Mathematical Society.
A. B. Cruzeiro
Universidade de Lisboa
We show that it is possible to associate diffusion processes to second order perturbations of the Ornstein-Uhlenbeck operator $L$ on the Wiener space of the form \begin{equation*} \mathcal{L}=L+ \frac12\sum_k \mathcal{L}_{\xi_k}^2 \end{equation*} where the $\xi_k$ are ``tangent processes'' (i.e., semimartingales with antisymmetric diffusion coefficients).
Keywords: Stochastic calculus of variations and the Malliavin calculus, operators on function spaces, stochastic processes
MSC numbers: 60H07, 47B38
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