XX: 01, 1-27, LNM 1204 (1986)
KNIGHT, Frank B.
Poisson representation of strict regular step filtrations
Retrieve article from Numdam
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 processesNature: Correction Retrieve article from Numdam
XX: 03, 30-33, LNM 1204 (1986)
MEYER, Paul-André
Sur l'existence de l'opérateur carré du champ Retrieve article from Numdam
XX: 04, 34-39, LNM 1204 (1986)
PONTIER, Monique;
STRICKER, Christophe;
SZPIRGLAS, Jacques
Sur le théorème de représentation par rapport à l'innovation Retrieve article from Numdam
XX: 05, 40-47, LNM 1204 (1986)
LIN, Cheng-De
Quand l'inégalité de Kunita-Watanabe est-elle une égalité ? Retrieve article from Numdam
XX: 06, 48-55, LNM 1204 (1986)
PARDOUX, Étienne
Grossissement d'une filtration et retournement du temps d'une diffusion Retrieve article from Numdam
XX: 07, 56-67, LNM 1204 (1986)
PICARD, Jean
Une classe de processus stable par retournement du temps Retrieve article from Numdam
XX: 08, 68-80, LNM 1204 (1986)
DOSS, Halim;
DOZZI, Marco
Estimation de grandes déviations pour les processus de diffusion à paramètre multidimensionnel Retrieve article from Numdam
XX: 09, 81-94, LNM 1204 (1986)
MAZZIOTTO, Gérald;
MILLET, Annie
Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal Retrieve article from Numdam
XX: 10, 95-100, LNM 1204 (1986)
KASPI, Haya;
MAISONNEUVE, Bernard
Predictable local times and exit systems Retrieve article from Numdam
XX: 11, 101-130, LNM 1204 (1986)
NORRIS, James R.
Simplified Malliavin calculus Retrieve article from Numdam
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 lawsNature: Original Retrieve article from Numdam
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 champNature: Original Retrieve article from Numdam
XX: 14, 186-312, LNM 1204 (1986)
MEYER, Paul-André
Élements de probabilités quantiques (chapters I to V) Retrieve article from Numdam
XX: 15, 313-316, LNM 1204 (1986)
JOURNÉ, Jean-Lin;
MEYER, Paul-André
Une martingale d'opérateurs bornés, non représentable en intégrale stochastique Retrieve article from Numdam
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 Retrieve article from Numdam
XX: 17, 321-330, LNM 1204 (1986)
MEYER, Paul-André
Quelques remarques au sujet du calcul stochastique sur l'espace de Fock Retrieve article from Numdam
XX: 18, 331-333, LNM 1204 (1986)
PARTHASARATHY, Kalyanapuram Rangachari
Some additional remarks on Fock space stochastic calculus Retrieve article from Numdam
XX: 19, 334-337, LNM 1204 (1986)
MEYER, Paul-André;
ZHENG, Wei-An
Sur la construction de certaines diffusions Retrieve article from Numdam
XX: 20, 338-340, LNM 1204 (1986)
RUIZ DE CHAVEZ, Juan
Sur la positivité de certains opérateurs Retrieve article from Numdam
XX: 21, 341-348, LNM 1204 (1986)
CARLEN, Eric A.;
STROOCK, Daniel W.
An application of the Bakry-Émery criterion to infinite dimensional diffusions Retrieve article from Numdam
XX: 22, 349-351, LNM 1204 (1986)
YAN, Jia-An
A comparison theorem for semimartingales and its applications Retrieve article from Numdam
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
2612Keywords: Semimartingales in manifolds,
Martingales in manifolds,
Lie groupNature: Original Retrieve article from Numdam
XX: 24, 375-378, LNM 1204 (1986)
VECHT, D.P. van der
Ultimateness and the Azéma-Yor stopping time Retrieve article from Numdam
XX: 25, 379-395, LNM 1204 (1986)
NUALART, David
Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan Retrieve article from Numdam
XX: 26, 396-418, LNM 1204 (1986)
MORROW, Gregory J.;
SILVERSTEIN, Martin L.
Two parameter extension of an observation of Poincaré Retrieve article from Numdam
XX: 27, 419-422, LNM 1204 (1986)
SILVERSTEIN, Martin L.
Orthogonal polynomial martingales on spheres Retrieve article from Numdam
XX: 28, 423-425, LNM 1204 (1986)
CHUNG, Kai Lai
Remark on the conditional gauge theorem Retrieve article from Numdam
XX: 29, 426-446, LNM 1204 (1986)
MÉTIVIER, Michel
Quelques problèmes liés aux systèmes infinis de particules et leurs limites Retrieve article from Numdam
XX: 30, 447-464, LNM 1204 (1986)
LE GALL, Jean-François
Une approche élémentaire des théorèmes de décomposition de Williams Retrieve article from Numdam
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 $({\cal E}^x,\ x\in
R)$, 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 $(\tilde{\cal E}^x,\ x\in
R)$ 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,
FiltrationsNature: Original Retrieve article from Numdam
XX: 32, 503-514, LNM 1204 (1986)
NEVEU, Jacques
Processus ponctuels stationnaires asymptotiquement gaussiens et comportement asymptotique de processus de branchement spatiaux sur-critiques Retrieve article from Numdam
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-intersectionNature: Original Retrieve article from Numdam
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 ${\bf R}^2$ Retrieve article from Numdam
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 representationNature: Original proofs Retrieve article from Numdam
XX: 36, 553-571, LNM 1204 (1986)
DYNKIN, Eugene B.
Functionals associated with self-intersections of the planar Brownian motion Retrieve article from Numdam
XX: 37, 572-611, LNM 1204 (1986)
PAGÈS, Gilles
Un théorème de convergence fonctionnelle pour les intégrales stochastiques Retrieve article from Numdam
XX: 38, 612-613, LNM 1204 (1986)
CHARLOT, François
Sur la démonstration des formules en théorie discrète du potentiel Retrieve article from Numdam
XX: 39, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XVIII Retrieve article from Numdam
XX: 40, 614-614, LNM 1204 (1986)
BAKRY, Dominique
Correction au Séminaire XIX Retrieve article from Numdam
XX: 41, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XIX Retrieve article from Numdam
XX: 42, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XV Retrieve article from Numdam
XX: 43, 614-614, LNM 1204 (1986)
MEYER, Paul-André
Correction au Séminaire XVI Retrieve article from Numdam
