XXV: 01, 1-9, LNM 1485 (1991)
DELLACHERIE, Claude
Théorie non-linéaire du potentiel : Un principe unifié de domination et du maximum et quelques applications
Retrieve article from Numdam
XXV: 02, 10-23, LNM 1485 (1991)
ÉMERY, Michel
Quelques cas de représentation chaotique Retrieve article from Numdam
XXV: 03, 24-30, LNM 1485 (1991)
SCHÜRMANN, Michael
The Azéma martingales as components of quantum independent increment processes Retrieve article from Numdam
XXV: 04, 31-36, LNM 1485 (1991)
PARTHASARATHY, Kalyanapuram Rangachari
Realisation of a class of Markov processes through unitary evolutions in Fock space Retrieve article from Numdam
XXV: 05, 37-38, LNM 1485 (1991)
PARTHASARATHY, Kalyanapuram Rangachari
An additional remark on unitary evolutions in Fock space Retrieve article from Numdam
XXV: 06, 39-51, LNM 1485 (1991)
BHAT, B. V. Rajarama;
PARTHASARATHY, Kalyanapuram Rangachari
Generalized harmonic oscillators in quantum probability Retrieve article from Numdam
XXV: 07, 52-60, LNM 1485 (1991)
MEYER, Paul-André
Application du ``bébé Fock'' au modèle d'Ising Retrieve article from Numdam
XXV: 08, 61-78, LNM 1485 (1991)
MEYER, Paul-André;
YAN, Jia-An
Les ``fonctions caractéristiques'' des distributions sur l'espace de Wiener Retrieve article from Numdam
XXV: 09, 79-94, LNM 1485 (1991)
YAN, Jia-An
Notes on the Wiener semigroup and renormalization Retrieve article from Numdam
XXV: 10, 95-107, LNM 1485 (1991)
YAN, Jia-An
Some remarks on the theory of stochastic integration Retrieve article from Numdam
XXV: 11, 108-112, LNM 1485 (1991)
MEYER, Paul-André
Sur la méthode de L.~Schwartz pour les e.d.s. Retrieve article from Numdam
XXV: 12, 113-120, LNM 1485 (1991)
KARANDIKAR, Rajeeva L.
On almost sure convergence of modified Euler-Peano approximation of solution to an S.D.E. driven by a semimartingale Retrieve article from Numdam
XXV: 13, 121-137, LNM 1485 (1991)
KAWABATA, Shigetoku;
YAMADA, Toshio
On Newton's method for stochastic differential equations Retrieve article from Numdam
XXV: 14, 138-139, LNM 1485 (1991)
JACOD, Jean;
PROTTER, Philip
Une remarque sur les équations différentielles stochastiques à solutions markoviennes Retrieve article from Numdam
XXV: 15, 140-161, LNM 1485 (1991)
JACOD, Jean
Régularité d'ordre quelconque pour un modèle statistique filtré Retrieve article from Numdam
XXV: 16, 162-177, LNM 1485 (1991)
MÉMIN, Jean;
SŁOMIŃSKI, Leszek
Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques Retrieve article from Numdam
XXV: 17, 178-195, LNM 1485 (1991)
FERNIQUE, Xavier
Convergence en loi de fonctions aléatoires continues ou cadlag, propriétés de compacité des lois Retrieve article from Numdam
XXV: 18, 196-219, LNM 1485 (1991)
PICARD, Jean
Calcul stochastique avec sauts sur une variété (
Stochastic differential geometry)
It is known from Meyer
1505 that intrinsic Ito integrals have a meaning for continuous semimartingales in a manifold $M$, provided $M$ is endowed with a connection. This is extended here to càdlàg semimartingales. The manifold must be endowed with a richer structure, a ``connector'', mapping $M\times M$ to the tangent bundle, that allows to interpret a jump $(X_{t-},X_t)$ as a tangent vector to $M$ at $X{t-}$; the differential of the connector at the diagonal reduces to a classical torsion-free connection. Introducing torsions leads to a more general ``transporter'', describing how parallel transports should behave at jump times, and reducing to a classical connection for infinitesimal jumps. Discrete-time approximations are established.
Keywords: Semimartingales in manifolds,
Martingales in manifolds,
JumpsNature: Original Retrieve article from Numdam
XXV: 19, 220-233, LNM 1485 (1991)
ÉMERY, Michel;
MOKOBODZKI, Gabriel
Sur le barycentre d'une probabilité dans une variété (
Stochastic differential geometry)
In a manifold $V$ (endowed with a connection), convex functions and continuous martingales can be defined, but expectations cannot. This article proposes to define the mass-centre of a probability $\mu$ on $V$ as a whole set of points, consisting of all $x$ in $V$ such that $f(x)\le\mu(f)$ for all bounded, convex $f$ on $V$. If $V$ is small enough, it is shown that this is equivalent to demanding that there exists (on a suitable filtered probability space) a continuous martingale $X$ such that $X_0=x$ and $X_1$ has law $\mu$
Comment: The conjecture (due to Émery) at the bottom of page 232 has been disproved by Kendall (
J. London Math. Soc. 46, 1992), as pointed out in
2650Keywords: Martingales in manifolds,
Convex functionsNature: Original Retrieve article from Numdam
XXV: 20, 234-261, LNM 1485 (1991)
BAKRY, Dominique
Inégalités de Sobolev faibles : un critère $\Gamma_2$ Retrieve article from Numdam
XXV: 21, 262-269, LNM 1485 (1991)
KARANDIKAR, Rajeeva L.
Multiplicative decomposition of nonsingular matrix valued semimartingales Retrieve article from Numdam
XXV: 22, 270-283, LNM 1485 (1991)
SOLÉ, Josep Lluis;
UTZET, Frederic
Intégrale multiple de Stratonovich pour le processus de Poisson Retrieve article from Numdam
XXV: 23, 284-290, LNM 1485 (1991)
DUBINS, Lester E.;
ÉMERY, Michel;
YOR, Marc
A continuous martingale in the plane that may spiral away to infinity Retrieve article from Numdam
XXV: 24, 291-310, LNM 1485 (1991)
ROELLY, Sylvie;
ZESSIN, Hans
Sur la mécanique statistique d'une particule brownienne sur le tore Retrieve article from Numdam
XXV: 25, 311-315, LNM 1485 (1991)
WEBER, Michel
New sufficient conditions for the law of the iterated logarithm in Banach spaces Retrieve article from Numdam
XXV: 26, 316-323, LNM 1485 (1991)
FUCHS, Aimé;
LETTA, Giorgio
Un résultat élémentaire de fiabilité. Application à la formule de Weierstrass sur la fonction gamma Retrieve article from Numdam
XXV: 27, 324-329, LNM 1485 (1991)
OGAWA, Shigeyoshi
Stochastic integral equations for the random fields Retrieve article from Numdam
XXV: 28, 330-344, LNM 1485 (1991)
BERTOIN, Jean
Décomposition du mouvement brownien avec dérive en un minimum local par juxtaposition de ses excursions positives et négatives Retrieve article from Numdam
XXV: 29, 345-348, LNM 1485 (1991)
BALDI, Paolo;
SANZ-SOLÉ, Marta
Une remarque sur la théorie des grandes déviations Retrieve article from Numdam
XXV: 30, 349-353, LNM 1485 (1991)
GOSWAMI, Alok;
RAO, B.V.
On filtrations of Brownian polynomials Retrieve article from Numdam
XXV: 31, 354-373, LNM 1485 (1991)
KÜCHLER, Uwe;
NEUMANN, Kirsten
An extension of Krein's inverse spectral theorem to strings with nonreflective left boundaries Retrieve article from Numdam
XXV: 32, 374-406, LNM 1485 (1991)
ALBEVERIO, Sergio;
MA, Zhi-Ming
Necessary and sufficient conditions for the existence of $m$-perfect processes associated with Dirichlet forms Retrieve article from Numdam
XXV: 33, 407-424, LNM 1485 (1991)
ROSEN, Jay S.
Second order limit laws for the local times of stable processes (
Limit theorems)
Using the method of moments, a central limit theorem is established for the increments $L^x_t-L^0_t$ of the local times of a symmetric $\beta$-stable process ($\beta>1$). The limit law is that of a fractional Brownian sheet, with Hurst index $\beta-1$, time-changed via $L_t^0$ in its time variable
Comment: Another proof due to Eisenbaum
3120 uses Dynkin's isomorphism. Ray-Knight theorems for these local times can be found in Eisenbaum-Kaspi-Marcus-Rosen-Shi
Ann. Prob. 28 (2000). A good reference on this subject is Marcus-Rosen,
Markov Processes, Gaussian Processes, and Local Times, Cambridge University Press (2006)
Keywords: Local times,
Stable processes,
Method of moments,
Fractional Brownian motion,
Brownian sheetNature: Original Retrieve article from Numdam
XXV: 34, 425-426, LNM 1485 (1991)
MEYER, Paul-André
Sur deux estimations d'intégrales multiples Retrieve article from Numdam
XXV: 35, 427-427, LNM 1485 (1991)
MEYER, Paul-André
Correction au Séminaire XXII Retrieve article from Numdam
XXV: 36, 427-427, LNM 1485 (1991)
YAN, Jia-An
Correction au Séminaire XXIII Retrieve article from Numdam
XXV: 37, 427-427, LNM 1485 (1991)
PARTHASARATHY, Kalyanapuram Rangachari
Correction au Séminaire XXIV Retrieve article from Numdam
