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November 2009 Hiding a drift
Miklós Rásonyi, Walter Schachermayer, Richard Warnung
Ann. Probab. 37(6): 2459-2479 (November 2009). DOI: 10.1214/09-AOP469

Abstract

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.

Citation

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Miklós Rásonyi. Walter Schachermayer. Richard Warnung. "Hiding a drift." Ann. Probab. 37 (6) 2459 - 2479, November 2009. https://doi.org/10.1214/09-AOP469

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1193.60073
MathSciNet: MR2573564
Digital Object Identifier: 10.1214/09-AOP469

Subjects:
Primary: 60G44, 60H05
Secondary: 60G05, 60H10

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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