Illinois Journal of Mathematics

Hiding a constant drift—a strong solution

Vilmos Prokaj and Walter Schachermayer

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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

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

First available in Project Euclid: 24 September 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60G44: Martingales with continuous parameter 60J65: Brownian motion [See also 58J65]
Secondary: 60G05: Foundations of stochastic processes 60H10: Stochastic ordinary differential equations [See also 34F05]


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.

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