## Illinois Journal of Mathematics

### Hiding a constant drift—a strong solution

#### Abstract

Let $B$ be a Brownian motion. We show that there is a process $H$ predictable in the natural filtration of $B$, such that $H⋅S$ is a Brownian motion in its own filtration, where $S_t = B_t + t$. In other words, $H$ hides the constant drift. This gives a positive answer to a question posed by Marc Yor.

#### Article information

Source
Illinois J. Math., Volume 54, Number 4 (2010), 1463-1480.

Dates
First available in Project Euclid: 24 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1348505537

Digital Object Identifier
doi:10.1215/ijm/1348505537

Mathematical Reviews number (MathSciNet)
MR2981856

Zentralblatt MATH identifier
1259.60056

#### Citation

Prokaj, Vilmos; Schachermayer, Walter. Hiding a constant drift—a strong solution. Illinois J. Math. 54 (2010), no. 4, 1463--1480. doi:10.1215/ijm/1348505537. https://projecteuclid.org/euclid.ijm/1348505537

#### References

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• M. Rásonyi, W. Schachermayer and R. Warnung, Hiding a drift, Ann. Probab. 37 (2009), 2459–2479.
• D. Revuz and M. Yor, Continuous martingales and Brownian motion, 3rd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1999.