منابع مشابه
Hiding a Drift
In this article we consider a Brownian motion with drift of the form dSt = μtdt+ dBt for t ≥ 0, with a specific non-trivial (μt)t≥0, predictable with respect to 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 F , such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermore, for any δ > 0, we...
متن کاملHiding a constant drift
The following question is due to Marc Yor: Let B be a Brownian motion and St = t+Bt. Can we define an F-predictable 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-predictability of H we can give a positive answer to this question. ...
متن کاملHiding a Constant Drift—a Strong Solution
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 St =Bt+t. In other words, H hides the constant drift. This gives a positive answer to a question posed by Marc Yor.
متن کامل00 8 Hiding the Drift
In this article we consider a Brownian motion with drift, denoted by S = (St)t≥0, of the form dSt = μtdt+ dBt for t ≥ 0, with a specific non-trivial drift predictable with respect to F , the natural filtration of the Brownian motion B = (Bt)t≥0. We construct a process H = (Ht)t≥0, also predictable with respect to F , such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermor...
متن کاملHIDING THE DRIFT 3 Proposition
In this article we consider a Brownian motion with drift, denoted by S = (St)t≥0, of the form dSt = μtdt+ dBt for t ≥ 0, with a specific non-trivial drift predictable with respect to F , the natural filtration of the Brownian motion B = (Bt)t≥0. We construct a process H = (Ht)t≥0 also predictable with respect to F B such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermore...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/09-aop469