A free Girsanov property for free Brownian motions

A "free Girsanov" property is proved for free Brownian motions. It is reminiscent of the classical Girsanov theorem in probability theory. In the free probability context, we prove that if (sigma(s))(s is an element of R+) is a free Brownian motion in (M, tau), if x is a process free from the sigma(s), if (sigma) over bar (s) = sigma(s) + integral(s)(0) x(u)du, then there is a trace (tau) over tilde such that((sigma) over tilde)(s is an element of R+) is a free Brownian motion for (tau) over tilde and the two traces are "asymptotically equivalent". This means that tau respectively (tau) over bar are asymptotic limits of states Psi(n) respectively (Psi) over tilde (n) and that for each n (Psi) over tilde (n) is obtained from Psi(n) by a change of probability given by an exponential density.