Hiding a constant drift

Vilmos Prokaj; Miklos Rasonyi; Walter Schachermayer

doi:10.1214/10-AIHP363

Hiding a constant drift

Vilmos Prokaj, Miklos Rasonyi, Walter Schachermayer

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

The following question is due to Marc Yor: Let B be a Brownian motion and S-t = t + B-t. Can we define an F-B - predictable process process H such that the resulting stochastic integral (H . S) is a Brownian motion (without drift) in its own filtration, i.e. an F-(H.S)-Brownian motion?

In this paper we show that by dropping the requirement of F-B-predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor's question. The original question, i.e., existence of a strong solution, remains open.

Original language	English
Pages (from-to)	498-514
Number of pages	17
Journal	Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Volume	47
Issue number	2
DOIs	https://doi.org/10.1214/10-AIHP363
Publication status	Published - May 2011

Keywords / Materials (for Non-textual outputs)

Brownian motion with drift
Stochastic integral
Enlargement of filtration
STOCHASTIC DIFFERENTIAL-EQUATION

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10.1214/10-AIHP363

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title = "Hiding a constant drift",

abstract = "The following question is due to Marc Yor: Let B be a Brownian motion and S-t = t + B-t. Can we define an F-B - predictable process process H such that the resulting stochastic integral (H . S) is a Brownian motion (without drift) in its own filtration, i.e. an F-(H.S)-Brownian motion?In this paper we show that by dropping the requirement of F-B-predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor's question. The original question, i.e., existence of a strong solution, remains open.",

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T1 - Hiding a constant drift

AU - Prokaj, Vilmos

AU - Rasonyi, Miklos

AU - Schachermayer, Walter

PY - 2011/5

Y1 - 2011/5

N2 - The following question is due to Marc Yor: Let B be a Brownian motion and S-t = t + B-t. Can we define an F-B - predictable process process H such that the resulting stochastic integral (H . S) is a Brownian motion (without drift) in its own filtration, i.e. an F-(H.S)-Brownian motion?In this paper we show that by dropping the requirement of F-B-predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor's question. The original question, i.e., existence of a strong solution, remains open.

AB - The following question is due to Marc Yor: Let B be a Brownian motion and S-t = t + B-t. Can we define an F-B - predictable process process H such that the resulting stochastic integral (H . S) is a Brownian motion (without drift) in its own filtration, i.e. an F-(H.S)-Brownian motion?In this paper we show that by dropping the requirement of F-B-predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor's question. The original question, i.e., existence of a strong solution, remains open.

KW - Brownian motion with drift

KW - Stochastic integral

KW - Enlargement of filtration

KW - STOCHASTIC DIFFERENTIAL-EQUATION

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DO - 10.1214/10-AIHP363

M3 - Article

SN - 0246-0203

VL - 47

SP - 498

EP - 514

JO - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

IS - 2

ER -

Hiding a constant drift

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