The Annals of Probability

Hiding a drift

Miklós Rásonyi, Walter Schachermayer, and Richard Warnung

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In this article we consider a Brownian motion with drift of the form

dSt=μtdt+dBt  for t≥0,

with a specific nontrivial (μt)t≥0, predictable with respect to $\mathbb{F}^{B}$, the natural filtration of the Brownian motion B=(Bt)t≥0. We construct a process H=(Ht)t≥0, also predictable with respect to $\mathbb{F}^{B}$, such that ((HS)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 ]μδ, μ+δ[, for fixed μ>0.

Article information

Ann. Probab. Volume 37, Number 6 (2009), 2459-2479.

First available in Project Euclid: 16 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60G44: Martingales with continuous parameter
Secondary: 60G05: Foundations of stochastic processes 60H10: Stochastic ordinary differential equations [See also 34F05]

Brownian motion with drift stochastic integral enlargement of filtration Lévy transform


Rásonyi, Miklós; Schachermayer, Walter; Warnung, Richard. Hiding a drift. Ann. Probab. 37 (2009), no. 6, 2459--2479. doi:10.1214/09-AOP469.

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