Og. Smolyanov et H. Vonweizsacker, CHANGE OF MEASURES AND THEIR LOGARITHMIC DERIVATIVES UNDER SMOOTH TRANSFORMATIONS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(1), 1995, pp. 103-108
The main result of this Note is the general Girsanov-Ramer type formul
a (1). Here nu is a measure on a locally convex space E with a logarit
hmic derivative beta(nu) : H x E --> R of nu with respect to a Hilbert
space H subset of E. For the vector field h : E --> H we suppose that
there is a sufficiently smooth map F : R x E --> E such that F(0, x)
= x et F(1, x) = x + h(x). Under these assumptions(1) holds where U-h(
nu) is given by (2) where f(1)' is the partial derivative of F with re
spect to t.