Conditions for the Absolute Continuity of Two Diffusions

Consider two diffusion processes on the line. For each starting point x and each finite time t, consider the measures these processes induce in the space of continuous functions on [0, t]. Necessary and sufficient conditions on the generators are found for the induced measures to be mutually absolutely continuous for each x and t. If the first process is Brownian motion, the second one must be Brownian motion with drift , where is locally in and satisfies a certain growth condition at <!-- MATH $\pm \infty$ --> .