The following question is due to Marc Yor: Let B be a Brownian motion and St=t+Bt. Can we define an $\mathcal{F}^{B}$ -predictable process H such that the resulting stochastic integral (H⋅S) is a Brownian motion (without drift) in its own filtration, i.e. an $\mathcal{F}^{(H\cdot S)}$ -Brownian motion?
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In this paper we show that by dropping the requirement of $\mathcal{F}^{B}$ -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.
Publié le : 2011-05-15
Classification:
Brownian motion with drift,
Stochastic integral,
Enlargement of filtration,
60H05,
60G44,
60J65,
60G05,
60H10
@article{1300887279,
author = {Prokaj, Vilmos and R\'asonyi, Mikl\'os and Schachermayer, Walter},
title = {Hiding a constant drift},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 498-514},
language = {en},
url = {http://dml.mathdoc.fr/item/1300887279}
}
Prokaj, Vilmos; Rásonyi, Miklós; Schachermayer, Walter. Hiding a constant drift. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 498-514. http://gdmltest.u-ga.fr/item/1300887279/