XXXII: 19, 264-305, LNM 1686 (1998)
BARLOW, Martin T.;
ÉMERY, Michel;
KNIGHT, Frank B.;
SONG, Shiqi;
YOR, Marc
Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes (
Brownian motion,
Filtrations)
Tsirelson has shown that no Walsh's Brownian motion with three rays or more can live in a Brownian filtration (GAFA
7, 1997). Using his methods, the result is extended to spider martingales. A conjecture of M. Barlow is also proved: if $L$ is an honest time in a (possibly multidimensional) Brownian filtration, then ${\cal F}_{L+}$ is generated by ${\cal F}_{L}$ and at most one event. Last, it is shown that a Walsh's Brownian motion can live in the filtration generated by another Walsh's Brownian motion only if the former is obtained from the latter by aggregating rays
Comment: On Tsirelson's theorem, see also Tsirelson, ICM 1998 vol. III, and M. Émery,
Astérisque 282 (2002). A simplified proof of Barlow's conjecture is given in
3304. For more on Théorème 1 (Slutsky's lemma), see
3221 and
3325Keywords: Filtrations,
Spider martingales,
Walsh's Brownian motion,
Cosiness,
Slutsky's lemmaNature: New exposition of known results,
Original additions
Retrieve article from Numdam
XXXIII: 04, 217-220, LNM 1709 (1999)
DE MEYER, Bernard
Une simplification de l'argument de Tsirelson sur le caractère non-brownien des processus de Walsh (
Brownian motion,
Filtrations)
Barlow's conjecture is proved with a simpler argument than in
3219Keywords: Filtrations,
Spider martingalesNature: New proof of known results Retrieve article from Numdam
