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.
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Serlet, L. (2008). Creation or deletion of a drift on a Brownian trajectory. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_11
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DOI: https://doi.org/10.1007/978-3-540-77913-1_11
Publisher Name: Springer, Berlin, Heidelberg
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