Browse by: Author name - Classification - Keywords - Nature

12 matches found
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 times
Nature: Original
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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 transforms
Nature: Original
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XVII: 01, 1-14, LNM 986 (1983)
KNIGHT, Frank B.
A transformation from prediction to past of an $L^2$-stochastic process
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XVIII: 04, 56-69, LNM 1059 (1984)
KNIGHT, Frank B.
On the Ray topology
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XX: 01, 1-27, LNM 1204 (1986)
KNIGHT, Frank B.
Poisson representation of strict regular step filtrations
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XXVII: 06, 36-43, LNM 1557 (1993)
KNIGHT, Frank B.
Some remarks on mutual windings
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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
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XXVIII: 28, 334-334, LNM 1583 (1994)
KNIGHT, Frank B.
Erratum to Some remarks on mutual windings'' (volume~XXVII)
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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
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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 3325
Keywords: Filtrations, Spider martingales, Walsh's Brownian motion, Cosiness, Slutsky's lemma
Nature: New exposition of known results, Original additions
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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
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XXXII: 24, 343-375, LNM 1686 (1998)
KNIGHT, Frank B.
On the upcrossing chains of stopped Brownian motion
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