VIII: 10, 134-149, LNM 381 (1974)
KNIGHT, Frank B.
Existence of small oscillations at zeros of brownian motion (
Brownian motion)
The one-dimensional Brownian motion path is shown to have an abnormal behaviour (an ``iterated logarithm'' upper limit smaller than one) at uncountably many times on his set of zeros
Comment: This result may be compared to Kahane,
C.R. Acad. Sci. 248, 1974
Keywords: Law of the iterated logarithm,
Local timesNature: Original
Retrieve article from Numdam
XII: 31, 428-445, LNM 649 (1978)
KNIGHT, Frank B.
On the sojourn times of killed Brownian motion (
Brownian motion)
To be completed
Keywords: Sojourn times,
Laplace transformsNature: Original Retrieve article from Numdam
XVII: 01, 1-14, LNM 986 (1983)
KNIGHT, Frank B.
A transformation from prediction to past of an $L^2$-stochastic process Retrieve article from Numdam
XVIII: 04, 56-69, LNM 1059 (1984)
KNIGHT, Frank B.
On the Ray topology Retrieve article from Numdam
XX: 01, 1-27, LNM 1204 (1986)
KNIGHT, Frank B.
Poisson representation of strict regular step filtrations Retrieve article from Numdam
XXVII: 06, 36-43, LNM 1557 (1993)
KNIGHT, Frank B.
Some remarks on mutual windings Retrieve article from Numdam
XXVII: 15, 133-158, LNM 1557 (1993)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
YOR, Marc
Le théorème d'arrêt en une fin d'ensemble prévisible Retrieve article from Numdam
XXVIII: 28, 334-334, LNM 1583 (1994)
KNIGHT, Frank B.
Erratum to ``Some remarks on mutual windings'' (volume~XXVII) Retrieve article from Numdam
XXX: 20, 312-343, LNM 1626 (1996)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
MOKOBODZKI, Gabriel;
YOR, Marc
Sur les processus croissants de type injectif Retrieve article from Numdam
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
XXXII: 22, 316-327, LNM 1686 (1998)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
YOR, Marc
Quelques calculs de compensateurs impliquant l'injectivité de certains processus croissants Retrieve article from Numdam
XXXII: 24, 343-375, LNM 1686 (1998)
KNIGHT, Frank B.
On the upcrossing chains of stopped Brownian motion Retrieve article from Numdam
