SOME MARTINGALES RELATED TO THE INTEGRAL OF BROWNIAN-MOTION - APPLICATIONS TO THE PASSAGE TIMES AND TRANSIENCE

Let (B-t)(t greater than or equal to 0) be the standard linear Brownia n motion started at y and set X-t = x + integral(0)(t)B(s)ds, U-t = (X -t, B-t). In this paper we introduce some martingales related to the M arkov process (U-t)(t greater than or equal to 0), which allow us to c alculate explicitly the probability laws of several passage times asso ciated to U in a probabilistic way. With the aid of an appropriate sup ermartingale, we also establish the transience of the process (U-t)(t greater than or equal to 0).