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
1350Keywords: Enlargement of filtrations,
Honest timesNature: Original
Retrieve article from Numdam
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 representationNature: Original Retrieve article from Numdam
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
1518Keywords: $BMO$,
$H^1$ space,
Hardy spacesNature: Original Retrieve article from Numdam
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 processesNature: New proof of known results Retrieve article from Numdam
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 decompositionNature: Original Retrieve article from Numdam
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
Comment: See also
1516Keywords: Explicit laws,
Occupation times,
Enlargement of filtrations,
Williams decompositionNature: Original Retrieve article from Numdam
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 filtrationsNature: Original Retrieve article from Numdam
XXIV: 15, 227-265, LNM 1426 (1990)
JEULIN, Thierry;
YOR, Marc
Filtration des ponts browniens et équations différentielles stochastiques linéaires Retrieve article from Numdam
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 processesNature: Original Retrieve article from Numdam
XXVII: 08, 53-77, LNM 1557 (1993)
JEULIN, Thierry;
YOR, Marc
Moyennes mobiles et semimartingales 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
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: 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
