La question suivante a été posée par Marc Yor: Soit B un mouvement Brownien et St=t+Bt. Peut-on définir un processus H qui est -prévisible tel que l'intégrale stochastique (H⋅S) soit un mouvement Brownien (sans drift) pour sa propre filtration ? Dans cet article nous fournissons une réponse affirmative en relâchant la condition que H soit -prévisible. Autrement dit, nous montrons qu'il existe une solution faible pour cette question de Yor. La question originale (c'est à dire, l'existence d'une solution forte) reste ouverte.
The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -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.
@article{AIHPB_2011__47_2_498_0,
author = {Prokaj, Vilmos and R\'asonyi, Mikl\'os and Schachermayer, Walter},
title = {Hiding a constant drift},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {47},
year = {2011},
pages = {498-514},
doi = {10.1214/10-AIHP363},
mrnumber = {2814420},
zbl = {1216.60048},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2011__47_2_498_0}
}
Prokaj, Vilmos; Rásonyi, Miklós; Schachermayer, Walter. Hiding a constant drift. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) pp. 498-514. doi : 10.1214/10-AIHP363. http://gdmltest.u-ga.fr/item/AIHPB_2011__47_2_498_0/
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