## The absolute continuity of a measure induced by infinite dimensional stochastic differential equations

J. Math. Sci. Univ. Tokyo
Vol. 12 (2005), No. 1, Page 77--104.

Heya, Naoki
The absolute continuity of a measure induced by infinite dimensional stochastic differential equations
We study infinite dimensional stochastic differential equations of the type $dX_t=dW_t+A(X_t)dW_t+b(X_t)dt.$ In particular, it is shown that the distribution of $X_t$ is absolute continuous with respect to a Gaussian measure if the modified Malliavin covariance is non-degenarate. A sufficient condition for non-degeneracy of the modified Malliavin covariance is presented.