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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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XX: 02, 28-29, LNM 1204 (1986)
FAGNOLA, Franco; LETTA, Giorgio
Sur la représentation intégrale des martingales du processus de Poisson (Stochastic calculus, Point processes)
Dellacherie gave in 805 a proof by stochastic calculus of the previsible representation property for the Wiener and Poisson processes. A gap in this proof is filled in 928 for Brownian motion and here for Poisson processes
Keywords: Stochastic integrals, Previsible representation, Poisson processes
Nature: Correction
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XX: 03, 30-33, LNM 1204 (1986)
MEYER, Paul-André
Sur l'existence de l'opérateur carré du champ
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XX: 04, 34-39, LNM 1204 (1986)
PONTIER, Monique; STRICKER, Christophe; SZPIRGLAS, Jacques
Sur le théorème de représentation par rapport à l'innovation
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XX: 05, 40-47, LNM 1204 (1986)
LIN, Cheng-De
Quand l'inégalité de Kunita-Watanabe est-elle une égalité ?
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XX: 06, 48-55, LNM 1204 (1986)
PARDOUX, Étienne
Grossissement d'une filtration et retournement du temps d'une diffusion
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XX: 07, 56-67, LNM 1204 (1986)
PICARD, Jean
Une classe de processus stable par retournement du temps
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XX: 08, 68-80, LNM 1204 (1986)
DOSS, Halim; DOZZI, Marco
Estimation de grandes déviations pour les processus de diffusion à paramètre multidimensionnel
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XX: 09, 81-94, LNM 1204 (1986)
MAZZIOTTO, Gérald; MILLET, Annie
Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal
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XX: 10, 95-100, LNM 1204 (1986)
KASPI, Haya; MAISONNEUVE, Bernard
Predictable local times and exit systems
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XX: 11, 101-130, LNM 1204 (1986)
NORRIS, James R.
Simplified Malliavin calculus
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XX: 12, 131-161, LNM 1204 (1986)
BOULEAU, Nicolas; HIRSCH, Francis
Propriété d'absolue continuité dans les espaces de Dirichlet et applications aux équations différentielles stochastiques (Dirichlet forms, Malliavin's calculus)
This is the main result of the Bouleau-Hirsch approach'' to absolute continuity in Malliavin calculus (see The Malliavin calculus and related topics by D. Nualart, Springer1995). In the framework of Dirichlet spaces, a general criterion for absolute continuity of random vectors is established; it involves the image of the energy measure. This leads to a Lipschitzian functional calculus for the Ornstein-Uhlenbeck Dirichlet form on Wiener space, and gives absolute continuity of the laws of the solutions to some SDE's with coefficients that can be uniformly degenerate
Comment: These results are extended by the same authors in their book Dirichlet Forms and Analysis on Wiener Space, De Gruyter 1991
Keywords: Dirichlet forms, Carré du champ, Absolute continuity of laws
Nature: Original
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XX: 13, 162-185, LNM 1204 (1986)
BOULEAU, Nicolas; LAMBERTON, Damien
Théorie de Littlewood-Paley et processus stables (Applications of martingale theory, Markov processes)
Meyer' probabilistic approach to Littlewood-Paley inequalities (1010, 1510) is extended by replacing the underlying Brownian motion with a stable process. The following spectral multiplicator theorem is obtained: If $(P_t)_{t\geq 0}$ is a symmetric Markov semigroup with spectral representation $P_t=\int_{[0,\infty)}e^{-t\lambda} dE_{\lambda}$, and if $M$ is a function on $R_+$ defined by $M(\lambda)=\lambda\int_0^\infty r(y)e^{-y\lambda}dy,$ where $r(y)$ is bounded and Borel on $R_+$, then the operator $T_M=\int_{[0,\infty)}M(\lambda)dE_{\lambda},$ which is obviously bounded on $L^2$, is actually bounded on all $L^p$ spaces of the invariant measure, $1<p<\infty$. The method also leads to new Littlewood-Paley inequalities for semigroups admitting a carré du champ operator
Keywords: Littlewood-Paley theory, Semigroup theory, Riesz transforms, Stable processes, Inequalities, Singular integrals, Carré du champ
Nature: Original
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XX: 14, 186-312, LNM 1204 (1986)
MEYER, Paul-André
Élements de probabilités quantiques (chapters I to V)
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XX: 15, 313-316, LNM 1204 (1986)
JOURNÉ, Jean-Lin; MEYER, Paul-André
Une martingale d'opérateurs bornés, non représentable en intégrale stochastique
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XX: 16, 317-320, LNM 1204 (1986)
PARTHASARATHY, Kalyanapuram Rangachari
A remark on the paper Une martingale d'opérateurs bornés, non représentable en intégrale stochastique'', by J.L. Journé and P.A. Meyer
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XX: 17, 321-330, LNM 1204 (1986)
MEYER, Paul-André
Quelques remarques au sujet du calcul stochastique sur l'espace de Fock
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XX: 18, 331-333, LNM 1204 (1986)
PARTHASARATHY, Kalyanapuram Rangachari
Some additional remarks on Fock space stochastic calculus
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XX: 19, 334-337, LNM 1204 (1986)
MEYER, Paul-André; ZHENG, Wei-An
Sur la construction de certaines diffusions
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XX: 20, 338-340, LNM 1204 (1986)
RUIZ DE CHAVEZ, Juan
Sur la positivité de certains opérateurs
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XX: 21, 341-348, LNM 1204 (1986)
CARLEN, Eric A.; STROOCK, Daniel W.
An application of the Bakry-Émery criterion to infinite dimensional diffusions
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XX: 22, 349-351, LNM 1204 (1986)
YAN, Jia-An
A comparison theorem for semimartingales and its applications
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XX: 23, 352-374, LNM 1204 (1986)
HAKIM-DOWEK, M.; LÉPINGLE, Dominique
L'exponentielle stochastique des groupes de Lie (Stochastic differential geometry)
Given a Lie group $G$ and its Lie algebra $\cal G$, this article defines and studies the stochastic exponential of a (continuous) semimartingale $M$ in $\cal G$ as the solution in $G$ to the Stratonovich s.d.e. $dX = X dM$. The inverse operation (stochastic logarithm) is also considered; various formulas are established (e.g. the exponential of $M+N$). When $M$ is a local martingale, $X$ is a martingale for the connection such that $\nabla_A B=0$ for all left-invariant vector fields $A$ and $B$
Comment: See also Karandikar Ann. Prob. 10 (1982) and 1722. For a sequel, see Arnaudon 2612
Keywords: Semimartingales in manifolds, Martingales in manifolds, Lie group
Nature: Original
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XX: 24, 375-378, LNM 1204 (1986)
VECHT, D.P. van der
Ultimateness and the Azéma-Yor stopping time
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XX: 25, 379-395, LNM 1204 (1986)
NUALART, David
Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan
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XX: 26, 396-418, LNM 1204 (1986)
MORROW, Gregory J.; SILVERSTEIN, Martin L.
Two parameter extension of an observation of Poincaré
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XX: 27, 419-422, LNM 1204 (1986)
SILVERSTEIN, Martin L.
Orthogonal polynomial martingales on spheres
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XX: 28, 423-425, LNM 1204 (1986)
CHUNG, Kai Lai
Remark on the conditional gauge theorem
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XX: 29, 426-446, LNM 1204 (1986)
MÉTIVIER, Michel
Quelques problèmes liés aux systèmes infinis de particules et leurs limites
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XX: 30, 447-464, LNM 1204 (1986)
LE GALL, Jean-François
Une approche élémentaire des théorèmes de décomposition de Williams
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XX: 31, 465-502, LNM 1204 (1986)
McGILL, Paul
Integral representation of martingales in the Brownian excursion filtration (Brownian motion, Stochastic calculus)
An integral representation is obtained of all square integrable martingales in the filtration $({\cal E}^x,\ x\inR)$, where ${\cal E}^x$ denotes the Brownian excursion $\sigma$-field below $x$ introduced by D. Williams 1343, who also showed that every $({\cal E}^x)$ martingale is continuous
Comment: Another filtration $(\tilde{\cal E}^x,\ x\inR)$ of Brownian excursions below $x$ has been proposed by Azéma; the structure of martingales is quite diffferent: they are discontinuous. See Y. Hu's thesis (Paris VI, 1996), and chap.~16 of Yor, Some Aspects of Brownian Motion, Part~II, Birkhäuser, 1997
Keywords: Previsible representation, Martingales, Filtrations
Nature: Original
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XX: 32, 503-514, LNM 1204 (1986)
NEVEU, Jacques
Processus ponctuels stationnaires asymptotiquement gaussiens et comportement asymptotique de processus de branchement spatiaux sur-critiques
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XX: 33, 515-531, LNM 1204 (1986)
ROSEN, Jay S.
A renormalized local time for multiple intersections of planar Brownian motion (Brownian motion)
Using Fourier techniques, the existence of a renormalized local time for $n$-fold self-intersections of planar Brownian motion is obtained, thus extending the case $n=2$, obtained in the pioneering work of Varadhan (Appendix to Euclidean quantum field theory, by K.~Symanzik, in Local Quantum Theory, Academic Press, 1969)
Comment: Closely related to 2036. A general reference is Le Gall, École d'Été de Saint-Flour XX, Springer LNM 1527
Keywords: Local times, Self-intersection
Nature: Original
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XX: 34, 532-542, LNM 1204 (1986)
YOR, Marc
Précisions sur l'existence et la continuité des temps locaux d'intersection du mouvement brownien dans ${\bf R}^2$
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XX: 35, 543-552, LNM 1204 (1986)
YOR, Marc
Sur la représentation comme intégrales stochastiques des temps d'occupation du mouvement brownien dans ${\bf R}^d$ (Brownian motion)
Varadhan's renormalization result (Appendix to Euclidean quantum field theory, by K.~Symanzik, in Local Quantum Theory consists in centering certain sequences of Brownian functionals and showing $L^2$-convergence. The same results are obtained here by writing these centered functionals as stochastic integrals
Comment: One of mny applications of stochastic calculus to the existence and regularity of self-intersection local times. See Rosen's papers on this topic in general, and page 196 of Le Gall, École d'Été de Saint-Flour XX, Springer LNM 1527
Keywords: Local times, Self-intersection, Previsible representation
Nature: Original proofs
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XX: 36, 553-571, LNM 1204 (1986)
DYNKIN, Eugene B.
Functionals associated with self-intersections of the planar Brownian motion
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XX: 37, 572-611, LNM 1204 (1986)
PAGÈS, Gilles
Un théorème de convergence fonctionnelle pour les intégrales stochastiques
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XX: 38, 612-613, LNM 1204 (1986)
CHARLOT, François
Sur la démonstration des formules en théorie discrète du potentiel
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XX: 39, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XVIII
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XX: 40, 614-614, LNM 1204 (1986)
BAKRY, Dominique
Correction au Séminaire XIX
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XX: 41, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XIX
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XX: 42, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XV
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XX: 43, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XVI
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