On the non-existence of stationary diffusions which satisfy the Beneš condition
Abstract The one-dimensional diffusion x t satisfying d x t = f ( x t )d t + d w t , where w t is a standard Brownian motion and f ( x ) satisfies the Benes condition f ′( x ) + f 2 ( x ) = ax 2 + bx + c for all real x , is considered. It is shown that this diffusion does not admit a stationary probability measure except for the linear case f ( x ) = αx + β , α