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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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XVII: 02, 15-31, LNM 986 (1983)
LE GALL, Jean-François
Applications du temps local aux équations différentielles stochastiques unidimensionnelles
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XVII: 03, 32-61, LNM 986 (1983)
BARLOW, Martin T.; PERKINS, Edwin A.
Strong existence, uniqueness and non-uniqueness in an equation involving local time
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XVII: 04, 62-66, LNM 986 (1983)
PROTTER, Philip; SZNITMAN, Alain-Sol
An equation involving local time
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XVII: 05, 67-71, LNM 986 (1983)
PERKINS, Edwin A.
Stochastic integrals and progressive measurability. An example
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XVII: 06, 72-77, LNM 986 (1983)
WEINRYB, Sophie
Étude d'une équation différentielle stochastique avec temps local
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XVII: 07, 78-80, LNM 986 (1983)
YAN, Jia-An
Une remarque sur les solutions faibles des équations différentielles stochastiques unidimensionnelles
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XVII: 08, 81-88, LNM 986 (1983)
LE GALL, Jean-François; YOR, Marc
Sur l'équation stochastique de Tsirelson
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XVII: 09, 89-105, LNM 986 (1983)
YOR, Marc
Le drap brownien comme limite en loi des temps locaux linéaires (Brownian motion, Local time, Brownian sheet)
A central limit theorem is obtained for the increments $L^x_t-L^0_t$ of Brownian local times. The limiting process is expressed in terms of a Brownian sheet, independent of the initial Brownian motion
Comment: This type of result is closely related to the Ray-Knight theorems, which describe the law of Brownian local times considered at certain random times. This has been extended first by Rosen in 2533, where Brownian motion is replaced with a symmetric stable process, then by Eisenbaum 2926
Keywords: Brownian motion, Several parameter processes
Nature: Original
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XVII: 10, 106-116, LNM 986 (1983)
JACKA, Saul D.
A local time inequality for martingales
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XVII: 11, 117-120, LNM 986 (1983)
CHOU, Ching Sung
Sur certaines inégalités de théorie des martingales
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XVII: 12, 121-122, LNM 986 (1983)
YAN, Jia-An
Sur un théorème de Kazamaki-Sekiguchi
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XVII: 13, 123-124, LNM 986 (1983)
GEBUHRER, Marc Olivier
Sur les fonctions holomorphes à valeurs dans l'espace des martingales locales
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XVII: 14, 125-131, LNM 986 (1983)
PRATELLI, Maurizio
Majoration dans $L^p$ du type Métivier-Pellaumail pour les semimartingales
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XVII: 15, 132-157, LNM 986 (1983)
BICHTELER, Klaus; JACOD, Jean
Calcul de Malliavin pour les diffusions avec sauts : Existence d'une densité dans le cas unidimensionnel
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XVII: 16, 158-161, LNM 986 (1983)
LÉANDRE, Rémi
Un exemple en théorie des flots stochastiques
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XVII: 17, 162-178, LNM 986 (1983)
CALAIS, J.-Y.; GÉNIN, M.
Sur les martingales locales continues indexées par ${]}0,\infty{[}$
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XVII: 18, 179-184, LNM 986 (1983)
HE, Sheng-Wu; YAN, Jia-An; ZHENG, Wei-An
Sur la convergence des semimartingales continues dans ${\bf R}^n$ et des martingales dans une variété (Stochastic calculus, Stochastic differential geometry)
Say that a continuous semimartingale $X$ with canonical decomposition $X_0+M+A$ converges perfectly on an event $E$ if both $M_t$ and $\int_0^t|dA_s|$ have an a.s. limit on $E$ when $t\rightarrow \infty$. It is established that if $A_t$ has the form $\int_0^tH_sd[M,M]_s$, $X$ converges perfectly on the event $\{\sup_t|X_t|+\lim\sup_tH_t <\infty \}$. A similar (but less simple) statement is shown for multidimensional $X$; and an application is given to martingales in manifolds: every point of a manifold $V$ (with a connection) has a neighbourhood $U$ such that, given any $V$-valued martingale $X$, almost all paths of $X$ that eventually remain in $U$ are convergent
Comment: The latter statement (martingale convergence) is very useful; more recent proofs use convex functions instead of perfect convergence. The next talk 1719 is a small remark on perfect convergence
Keywords: Semimartingales, Martingales in manifolds
Nature: Original
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XVII: 19, 185-186, LNM 986 (1983)
ÉMERY, Michel
Note sur l'exposé précédent (Stochastic calculus)
A small remark on 1718: The event where a semimartingale converges perfectly is also the smallest (modulo negligibility) event where it is a semimartingale up to infinity
Keywords: Semimartingales
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XVII: 20, 187-193, LNM 986 (1983)
MEYER, Paul-André
Le théorème de convergence des martingales dans les variétés riemanniennes, d'après R.W. Darling et W.A. Zheng (Stochastic differential geometry)
Exposition of two results on the asymptotic behaviour of martingales in a Riemannian manifold: First, Darling's theorem says that on the event where the Riemannian quadratic variation $<X,X>_\infty$ of a martingale $X$ is finite, $X_\infty$ exists in the Aleksandrov compactification of $V$. Second, Zheng's theorem asserts that on the event where $X_\infty$ exists in $V$, the Riemannian quadratic variation $<X,X>_\infty$ is finite
Comment: Darling's result is in Publ. R.I.M.S. Kyoto 19 (1983) and Zheng's in Zeit. für W-theorie 63 (1983). As observed in He-Yan-Zheng 1718, a stronger version of Zheng's theorem holds (with the same argument): On the event where $X_\infty$ exists in $V$, $X$ is a semimartingale up to infinity (so for instance solutions to good SDE's driven by $X$ also have a limit at infinity)
Keywords: Martingales in manifolds
Nature: Exposition
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XVII: 21, 194-197, LNM 986 (1983)
PRICE, Gareth C.; WILLIAMS, David
Rolling with slipping': I (Stochastic calculus, Stochastic differential geometry)
If $Z$ and $\tilde Z$ are two Brownian motions on the unit sphere for the filtration of $Z$, there differentials $\partial Y=(\partial Z) \times Z$ (Stratonovich differentials and vector product) and $\partial\tilde Y$ (similarly defined) are related by $d\tilde Y = H dY$, where $H$ is a previsible, orthogonal transformation such that $HZ=\tilde Z$
Keywords: Brownian motion in a manifold, Previsible representation
Nature: Original
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XVII: 22, 198-204, LNM 986 (1983)
KARANDIKAR, Rajeeva L.
Girsanov type formula for a Lie group valued Brownian motion (Brownian motion, Stochastic differential geometry)
A formula for the change of measure of a Lie group valued Brownian motion is stated and proved. It needs a Borel correspondence between paths in the Lie algebra and paths in the group, that transforms all (continuous) semimartingales in the algebra into their stochastic exponential
Comment: For more on stochastic exponentials in Lie groups, see Hakim-Dowek-Lépingle 2023 and Arnaudon 2612
Keywords: Changes of measure, Brownian motion in a manifold, Lie group
Nature: Original
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XVII: 23, 205-220, LNM 986 (1983)
CHEN, Mu-Fa; STROOCK, Daniel W.
$\lambda_\pi$-invariant measures
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XVII: 24, 221-224, LNM 986 (1983)
BASS, Richard F.
Skorohod imbedding via stochastic integrals (Brownian motion)
A centered probability $\mu$ on $\bf R$ is the law of $g(X_1)$, for a suitable function $g$ and $(X_t,\ t\le 1)$ a Brownian motion. The martingale with terminal value $g(X_1)$ is a time change $(T(t), \ t\le1)$ of a Brownian motion $\beta$; it is shown that $T(1)$ is a stopping time for $\beta$, thus showing the Skorohod embedding for $\mu$
Comment: A general survey on the Skorohod embedding problem is Ob\lój, Probab. Surv. 1, 2004
Keywords: Skorohod imbedding
Nature: Original
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XVII: 25, 225-226, LNM 986 (1983)
MEILIJSON, Isaac
On the Azéma-Yor stopping time (Brownian motion)
Comment: A general survey on the Skorohod embedding problem is Ob\lój, Probab. Surv. 1, 2004
Keywords: Skorohod imbedding
Nature: Original
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XVII: 26, 227-239, LNM 986 (1983)
VALLOIS, Pierre
Le problème de Skorokhod sur $\bf R$ : une approche avec le temps local (Brownian motion)
A solution to Skorohod's embedding problem is given, using the first hiting time of a set by the 2-dimensional process which consists of Brownian motion and its local time at zero. The author's aim is to correct'' the asymmetry inherent to the Azéma-Yor construction
Comment: A general survey on the Skorohod embedding problem is Ob\lój, Probab. Surv. 1, 2004
Keywords: Skorohod imbedding, Local times
Nature: Original
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XVII: 27, 240-242, LNM 986 (1983)
HOLEWIJN, Petrus Johannes; MEILIJSON, Isaac
Note on the central limit theorem for stationary processes
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XVII: 28, 243-297, LNM 986 (1983)
ALDOUS, David J.
Random walks on finite groups and rapidly mixing Markov chains (Markov processes)
The mixing time'' for a Markov chain---how many steps are needed to approximately reach the stationary distribution---is defined here by taking the variation distance between measures and the worst possible starting point, and bounded above by coupling arguments. For the simple random walk on the discrete cube $\{0,1\}^d$ with large $d$, there is a cut-off phenomenon'', an abrupt change in variation distance from 1 to 0 around time $1/4\ d\,\log d$. For a natural model of riffle shuffle of an $n$-card deck, there is an analogous cut-off at time $3/2\ \log n$. The relationship between rapid mixing'' and approximate exponential distribution for first hitting times on small subsets, is also discussed
Comment: In the 1960s and 1970s, Markov chains were considered by probabilists as rather trite objects. This work was one of several papers that prompted a reassessment and focused attention on the question of mixing time. In 1981, Diaconis-Sashahani (Z. Wahrsch. Verw. Gebiete 57) had established the cut-off phenomenon for a different shuffling scheme. For a random walk on a graph, Alon (Combinatorica 6, 1986) related an eigenvalue-based mixing time to expansion properties of the graph, and parallel work of Lawler-Sokal (Trans. Amer. Math. Soc. 309, 1988) in the broader setting of reversible chains made a connection with models from statistical physics. Jerrum-Sinclair (Inform. and Comput. 82, 1989) gave the first deep use of Markov chain methods in the theory of algorithms, while Geman-Geman (IEEE Trans. Pattern Anal. Machine Intell. 6, 1984) promoted the use of Markov chains in image reconstruction. Such papers brought the attention of probabilists to the Metropolis algorithm in statistical physics, and foreshadowed the development of Markov chain Monte Carlo methods in Bayesian statistics, e.g. Smith (Philos. Trans. Roy. Soc. London 337, 1991)
Keywords: Markov chains, Hitting probabilities
Nature: Original
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XVII: 29, 298-305, LNM 986 (1983)
ABOULAÏCH, Rajae; STRICKER, Christophe
Variation des processus mesurables
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XVII: 30, 306-310, LNM 986 (1983)
ABOULAÏCH, Rajae; STRICKER, Christophe
Sur un théorème de Talagrand
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XVII: 31, 311-320, LNM 986 (1983)
PRATELLI, Maurizio
La classe des semimartingales qui permettent d'intégrer les processus optionnels
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XVII: 32, 321-345, LNM 986 (1983)
LENGLART, Érik
Désintégration régulière de mesure sans conditions habituelles
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XVII: 33, 346-348, LNM 986 (1983)
HE, Sheng-Wu
Some remarks on single jump processes
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XVII: 34, 349-352, LNM 986 (1983)
HE, Sheng-Wu
The representation of Poisson functionals
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XVII: 35, 353-370, LNM 986 (1983)
DOSS, Halim; PRIOURET, Pierre
Petites perturbations de systèmes dynamiques avec réflexion
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XVII: 36, 371-376, LNM 986 (1983)
MÉMIN, Jean
Sur la contiguïté relative de deux suites de mesures. Compléments
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XVII: 37, 377-383, LNM 986 (1983)
LEDOUX, Michel
Une remarque sur la convergence des martingales à deux indices
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XVII: 38, 384-397, LNM 986 (1983)
LEDOUX, Michel
Arrêt par régions de $\{S_{\bf n}/{\bf n},{\bf n}\in{\bf N}^2\}$
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XVII: 39, 398-417, LNM 986 (1983)
NUALART, David
Différents types de martingales à deux indices
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XVII: 40, 418-424, LNM 986 (1983)
MAZZIOTTO, Gérald
Régularité à droite des surmartingales à deux indices et théorème d'arrêt
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XVII: 41, 425-497, LNM 986 (1983)
Central limit problem and invariance principles on Banach spaces
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XVII: 42, 498-501, LNM 986 (1983)
BAKRY, Dominique
Une remarque sur les processus gaussiens définissant des mesures $L^2$
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XVII: 43, 502-507, LNM 986 (1983)
TALAGRAND, Michel
Processus canoniquement mesurables (ou : Doob avait raison)
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XVII: 44, 509-511, LNM 986 (1983)
JACOD, Jean; MÉMIN, Jean
Rectification à Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité
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XVII: 45, 512-512, LNM 986 (1983)
YAN, Jia-An
Correction au volume XVI
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XVII: 46, 512-512, LNM 986 (1983)
MEYER, Paul-André
Correction au volume XVI (supplément)
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XVII: 47, 512-512, LNM 986 (1983)
BARLOW, Martin T.
Correction to `$L(B_t,t)$ is not a semimartingale''
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