Logarithmic derivatives of diffusion measures in a Hilbert space (Q2730507)

If \(\mu\) is a measure on a Riemannian manifold, its logarithmic derivative (if it exists) is a vector field \(\Lambda\) defined by the formula NEWLINE\[NEWLINE \int_X(\Lambda (y),V(y)) d\mu (y)=-\int_X\operatorname{div}V(y) d\mu (y) NEWLINE\]NEWLINE that is valid for all vector fields \(V\), for which the right-hand side is defined. The author considers the logarithmic derivative \(\Lambda\) of the transition probability of a diffusion process on an infinite-dimensional Hilbert space. A sequence of vector fields on certain \(n\)-dimensional Riemannian manifolds converging to \(\Lambda\), as \(n\to \infty\), is constructed.