Abstract: | Let Xt be a one-dimensional diffusion of the form dXt=dBt+(Xt)dt. Let Tbe a fixed positive number and let be the diffusion process which is Xt conditioned so that X0=XT=x. If the drift is constant, i.e., , then the conditioned diffusion process is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property. |