The absolute continuity of a measure induced by infinite dimensional stochastic differential equations
Vol. 12 (2005), No. 1, Page 77--104.
Heya, Naoki
The absolute continuity of a measure induced by infinite dimensional stochastic differential equations
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Abstract:
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.
Mathematics Subject Classification (1991): 60H07
Mathematical Reviews Number: MR2126786
Received: 2004-08-26
