Abstract
Let Xt be a one-dimensional diffusion of the form dXt=dBt+μ(Xt)dt. Let Tbe a fixed positive number and let \(\bar X_t \) be the diffusion process which is Xt conditioned so that X0=XT=x. If the drift is constant, i.e., \(\mu (x) \equiv k\), then the conditioned diffusion process \(\bar X_t \) 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.
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