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Paper No. 08-01

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L Alili and P Patie

Boundary Crossing Identities for Self-Similar Diffusions having the time inversion property

Abstract: We review some functional transformations and apply them to derive some boundary crossing identities for Brownian motions and Bessel processes with wide drift and families of continuous curves. In the Brownian setting, we provide an interpretation of the results by the standard method of images. We also establish the exact asymptotics for large time of the densities under some additional conditions.