Hiding a constant drift
نویسندگان
چکیده
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. 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. AMS 2000 subject classifications: Primary 60H05, 60G44, 60J65; secondary 60G05, 60H10.
منابع مشابه
Hiding 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.
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تاریخ انتشار 2010