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Path transformations of first passage bridges. (English) Zbl 1061.60083

Summary: We define the first passage bridge from 0 to \(\lambda\) as the Brownian motion on the time interval \([0,1]\) conditioned to first hit \(\lambda\) at time 1. We show that this process may be related to the Brownian bridge, the Bessel bridge or the Brownian excursion via some path transformations, the main one being an extension of Vervaat’s transformation. We also propose an extension of these results to certain bridges with cyclically exchangeable increments.

MSC:

60J65 Brownian motion
60G09 Exchangeability for stochastic processes
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