Limit theorems for a Brownian motion with drift in a white noise environment

This paper discusses limit theorems for a diffusion analogue of Kesten-Kozlov-Spitzerʹs random walk in a random environment. The results obtained are similar to theirs but can be presented in a more explicit form by the use of Kreinʹs spectral theory for one-dimensional generalized second-order differential operators of the form d/dMd/dx.