Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2001; 38(2): 311-319

Printed March 1, 2001

Copyright © The Korean Mathematical Society.

Construction of some processes on the Wiener space associated to second order operators

A. B. Cruzeiro

Universidade de Lisboa

Abstract

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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