Creation or deletion of a drift on a Brownian trajectory

Abstract

We show that a negative drift can be created on a Brownian trajectory by cutting excursions according to a certain Poisson measure. Conversely a negative drift can be annihilated by inserting independent excursions again according to a certain Poisson measure. We first give results in discrete time by considering the random walks as contour processes of Galton-Watson trees and then pass to the limit. © 2008 Springer-Verlag Berlin Heidelberg.