Conditioned Diffusions which are Brownian Bridges

Itai Benjamini and Susan Lee ()

Journal of Theoretical Probability, 1997, vol. 10, issue 3, 733-736

Abstract: Abstract Let X t be a one-dimensional diffusion of the form dX t=dB t+μ(X t)dt. Let Tbe a fixed positive number and let $$\bar X_t $$ be the diffusion process which is X t conditioned so that X 0=X T=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.

Keywords: Diffusions; Brownian motion; Brownian bridge; Girsanov transformations (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022657828923

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