Hiding a drift

Abstract

In this article we consider a Brownian motion with drift of the form dSt = μt dt +dBt for t ≥ 0, with a specific nontrivial (μt)t≥0, predictable with respect to F{double-struck}B, the natural filtration of the Brownian motion B = (Bt)t≥0. We construct a process H = (Ht)t≥0, also predictable with respect to F{double-struck}B, such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermore, for any δ > 0, we refine this construction such that the drift (μt)t≥0 only takes values in ]μ - δ, μ+ δ[, for fixed μ>0. © Institute of Mathematical Statistics, 2009.