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13 matches found
XII: 11, 78-97, LNM 649 (1978)
JEULIN, Thierry; YOR, Marc
Grossissement d'une filtration et semi-martingales~: Formules explicites (General theory of processes)
This contains very substantial improvements on 1209, namely, the explicit computation of the characteristics of the semimartingales involved
Comment: For additional results on enlargements, see the two Lecture Notes volumes 833 (T. Jeulin) and 1118. See also 1350
Keywords: Enlargement of filtrations, Honest times
Nature: Original
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XIII: 29, 332-359, LNM 721 (1979)
JEULIN, Thierry; YOR, Marc
Inégalité de Hardy, semimartingales, et faux-amis (Martingale theory, General theory of processes)
The main purpose of this paper is to warn against obvious'' statements which are in fact false. Let $({\cal G}_t)$ be an enlargement of $({\cal F}_t)$. Assume that ${\cal F}$ has the previsible representation property with respect to a martingale $X$ which is a ${\cal G}$-semimartingale. Then it does not follow that every ${\cal F}$-martingale $Y$ is a ${\cal G}$-semimartingale. Also, even if $Y$ is a ${\cal G}$-semimartingale, its ${\cal G}$-compensator may have bad absolute continuity properties. The counterexample to the first statement involves a detailed study of the initial enlargement of the filtration of Brownian motion $(B_t)_{t\le 1}$ by the random variable $B_1$, which transforms it into the Brownian bridge, a semimartingale. Then the stochastic integrals with respect to $B$ which are ${\cal G}$-semimartingales are completely described, and this is the place where the classical Hardy inequality appears
Keywords: Hardy's inequality, Previsible representation
Nature: Original
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XIII: 30, 360-370, LNM 721 (1979)
JEULIN, Thierry; YOR, Marc
Sur l'expression de la dualité entre $H^1$ et $BMO$ (Martingale theory)
The problem is to find pairs of martingales $X,Y$ belonging to $H^1$ and $BMO$ such that the duality functional can be expressed as $E[X_{\infty}Y_{\infty}]$
Comment: On the same topic see 1518
Keywords: $BMO$, $H^1$ space, Hardy spaces
Nature: Original
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XIII: 45, 521-532, LNM 721 (1979)
JEULIN, Thierry
Un théorème de J.W. Pitman (Brownian motion, Diffusion theory)
This paper contains an appendix by M. Yor. Let $(B_t)$ and $(Z_t)$ be a Brownian motion and a Bes$_3$ process both starting at $0$. Put $S_t=\sup_{s\le t} B_t$ and $J_t=\inf_{s\ge t}Z_t$. Then Pitman's theorem asserts that, in law, $2S-B=Z$ and $2J-Z=B$ (both statements being in fact equivalent). A complete proof of the theorem is given, using techniques from the general theory of processes. The appendix shows that, granted that $2S-B$ is Markov, it is easy to see that it is a Bes$_3$
Keywords: Bessel processes
Nature: New proof of known results
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XIII: 50, 574-609, LNM 721 (1979)
JEULIN, Thierry
Grossissement d'une filtration et applications (General theory of processes, Markov processes)
This is a sequel to the papers 1209 and 1211, giving mostly applications of the theory of enlargements (turning a honest time $L$ into a stopping time) to Markov processes. The paper begins with a computation of conditional expectations relative to ${\cal F}_{L-}$, ${\cal F}_{L}$, ${\cal F}_{L+}$. This result is applied to coterminal times of a Markov process. Again a section is devoted to a general computation on two successive enlargements, which is shown to imply (with some work) Williams' well-known decomposition of Brownian paths
Keywords: Enlargement of filtrations, Williams decomposition
Nature: Original
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XV: 15, 210-226, LNM 850 (1981)
JEULIN, Thierry; YOR, Marc
Sur les distributions de certaines fonctionnelles du mouvement brownien (Brownian motion)
This paper gives new proofs and extensions of results due to Knight, concerning occupation times by the process $(S_t,B_t)$ up to time $T_a$, where $(B_t)$ is Brownian motion, $T_a$ the hitting time of $a$, and $(S_t)$ is $\sup_{s\le t} B_s$. The method uses enlargement of filtrations, and martingales similar to those of 1306. Theorem 3.7 is a decomposition of Brownian paths akin to Williams' decomposition
Keywords: Explicit laws, Occupation times, Enlargement of filtrations, Williams decomposition
Nature: Original
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XVI: 22, 248-256, LNM 920 (1982)
JEULIN, Thierry
Sur la convergence absolue de certaines intégrales (General theory of processes)
This paper is devoted to the a.s. absolute convergence of certain random integrals, a classical example of which is $\int_0^t ds/|B_s|^{\alpha}$ for Brownian motion starting from $0$. The author does not claim to prove deep results, but his technique of optional increasing reordering (réarrangement) of a process should be useful in other contexts too
Comment: This paper greatly simplifies a proof in the author's Semimartingales et Grossissement de Filtrations, LNM 833, p.44
Keywords: Enlargement of filtrations
Nature: Original
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XXIV: 15, 227-265, LNM 1426 (1990)
JEULIN, Thierry; YOR, Marc
Filtration des ponts browniens et équations différentielles stochastiques linéaires
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XXVI: 24, 322-347, LNM 1526 (1992)
JEULIN, Thierry; YOR, Marc
Une décomposition non-canonique du drap brownien (Brownian sheet, Gaussian processes)
In 2415, the authors have introduced a transform of Brownian motion. Here, a similar transform is defined on the Brownian sheet; this transform is shown to be strongly mixing
Comment: This work was motivated by Föllmer's article on Martin boundaries on Wiener space (in Diffusion processes and related problems in analysis, vol.~I, Birkhäuser 1990)
Keywords: Brownian motion, Several parameter processes
Nature: Original
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XXVII: 08, 53-77, LNM 1557 (1993)
JEULIN, Thierry; YOR, Marc
Moyennes mobiles et semimartingales
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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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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: 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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