Recurrence of a diffusion process in a multidimensional Brownian environment (Q1327789)

The author considers diffusion processes on \(\mathbb{R}^ d\) with generators \({1\over 2} (\Delta- \nabla W\cdot\nabla)\), where \(W\) is a Brownian motion with \(d\)-dimensional time. It is proved that for almost all trajectories of \(W\) the corresponding diffusion is recurrent.