XIX: 01, 1-11, LNM 1123 (1985)
NELSON, Edward
Critical diffusions
Retrieve article from Numdam
XIX: 02, 12-26, LNM 1123 (1985)
MEYER, Paul-André;
ZHENG, Wei-An
Construction de processus de Nelson réversibles Retrieve article from Numdam
XIX: 03, 27-36, LNM 1123 (1985)
DURRETT, Richard T.
On the unboundedness of martingale transforms Retrieve article from Numdam
XIX: 04, 37-62, LNM 1123 (1985)
HAUSSMANN, Ulrich G.
L'équation de Zakai et le problème séparé du contrôle optimal stochastique Retrieve article from Numdam
XIX: 05, 63-79, LNM 1123 (1985)
SALMINEN, Paavo
On local times of a diffusion Retrieve article from Numdam
XIX: 06, 80-90, LNM 1123 (1985)
HADJIEV, Dimitar I.
The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps Retrieve article from Numdam
XIX: 07, 91-112, LNM 1123 (1985)
SCHWARTZ, Laurent
Construction directe d'une diffusion sur une variété (
Stochastic differential geometry)
This seems to be the first use of Witney's embedding theorem to construct a process (a Brownian motion, a diffusion, a solution to some s.d.e.) in a manifold $M$ by embedding $M$ into some $
R^d$. Very general existence and uniqueness results are obtained
Comment: This method has since become standard in stochastic differential geometry; see for instance Émery's book
Stochastic Calculus in Manifolds (Springer, 1989)
Keywords: Diffusions in manifolds,
Stochastic differential equationsNature: Original Retrieve article from Numdam
XIX: 08, 113-129, LNM 1123 (1985)
MEYER, Paul-André
Sur la théorie de Littlewood-Paley-Stein, d'après Coifman-Rochberg-Weiss et Cowling Retrieve article from Numdam
XIX: 09, 130-174, LNM 1123 (1985)
BAKRY, Dominique
Transformation de Riesz pour les semi-groupes symétriques (two parts) Retrieve article from Numdam
XIX: 10, 175-175, LNM 1123 (1985)
BAKRY, Dominique
Une remarque sur les inégalités de Littlewood-Paley sous l'hypothèse $\Gamma_2\ge0$ Retrieve article from Numdam
XIX: 11, 176-176, LNM 1123 (1985)
MEYER, Paul-André
Une remarque sur la topologie fine Retrieve article from Numdam
XIX: 12, 177-206, LNM 1123 (1985)
BAKRY, Dominique;
ÉMERY, Michel
Diffusions hypercontractives Retrieve article from Numdam
XIX: 13, 207-208, LNM 1123 (1985)
KÔNO, Norio
Démonstration probabiliste du théorème de d'Alembert Retrieve article from Numdam
XIX: 14, 209-217, LNM 1123 (1985)
STRICKER, Christophe
Lois de semimartingales et critères de compacité Retrieve article from Numdam
XIX: 15, 218-221, LNM 1123 (1985)
STRICKER, Christophe
Une remarque sur une certaine classe de semimartingales Retrieve article from Numdam
XIX: 16, 222-229, LNM 1123 (1985)
DELLACHERIE, Claude
Quelques résultats sur les maisons de jeu analytiques Retrieve article from Numdam
XIX: 17, 230-241, LNM 1123 (1985)
RUIZ DE CHAVEZ, Juan
Espaces de Fock pour les procesus de Wiener et de Poisson Retrieve article from Numdam
XIX: 18, 242-247, LNM 1123 (1985)
RUIZ DE CHAVEZ, Juan
Compensation multiplicative et ``produits de Wick'' Retrieve article from Numdam
XIX: 19, 248-257, LNM 1123 (1985)
RUIZ DE CHAVEZ, Juan
Sur les intégrales stochastiques multiples Retrieve article from Numdam
XIX: 20, 258-262, LNM 1123 (1985)
PERKINS, Edwin A.
Multiple stochastic integrals---a counter example Retrieve article from Numdam
XIX: 21, 263-270, LNM 1123 (1985)
LÉANDRE, Rémi
Estimation dans $L^p({\bf R}^n)$ de la loi de certains processus à accroissements indépendants Retrieve article from Numdam
XIX: 22, 271-274, LNM 1123 (1985)
LÉANDRE, Rémi
Flot d'une équation différentielle stochastique avec semimartingale directrice discontinue (
Stochastic calculus)
Given a good s.d.e. of the form $dX=F\circ X_- dZ$, $X_{t-}$ is obtained from $X_t$ by computing $H_z(x) = x+F(x)z$, where $z$ stands for the jump of $Z$. Call $D$ (resp. $I$ the set of all $z$ such that $H_z$ is a diffeomorphism (resp. injective). It is shown that the flow associated to the s.d.e. is made of diffeomorphisms (respectively is one-to-one) iff all jumps of $Z$ belong to $D$ (resp. $I$)
Keywords: Stochastic differential equations,
Flow of a s.d.e.Nature: Original Retrieve article from Numdam
XIX: 23, 275-277, LNM 1123 (1985)
KAZAMAKI, Norihiko
A counterexample related to $A_p$-weights in martingale theory Retrieve article from Numdam
XIX: 24, 278-284, LNM 1123 (1985)
DUFFIE, Darrell
Predictable representation of martingale spaces and changes of probability measures Retrieve article from Numdam
XIX: 25, 285-290, LNM 1123 (1985)
DINCULEANU, Nicolae
Weak compactness in the space $H^1$ of martingales Retrieve article from Numdam
XIX: 26, 291-296, LNM 1123 (1985)
BIANE, Philippe
Comparaison entre temps d'atteinte et temps de séjour de certaines diffusions réelles Retrieve article from Numdam
XIX: 27, 297-313, LNM 1123 (1985)
LE GALL, Jean-François
Sur la mesure de Hausdorff de la courbe brownienne (
Brownian motion)
Previous results on the $h$-measure of the Brownian curve in $
R^2$ or $
R^3$ indexed by $t\in[0,1]$, by Cisielski-Taylor
Trans. Amer. Math. Soc. 103 (1962) and Taylor
Proc. Cambridge Philos. Soc. 60 (1964) are sharpened. The method uses the description à la Ray-Knight of the local times of Bessel processes
Comment: These Ray-Knight descriptions are useful ; they were later used in questions not related to Hausdorff measures. See for instance Biane-Yor,
Ann. I.H.P. 23 (1987), Yor,
Ann. I.H.P. 27 (1991)
Keywords: Hausdorff measures,
Brownian motion,
Bessel processes,
Ray-Knight theoremsNature: Original Retrieve article from Numdam
XIX: 28, 314-331, LNM 1123 (1985)
LE GALL, Jean-François
Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan (
Brownian motion)
The normalized self-intersection local time of planar Brownian motion was shown to exist by Varadhan (Appendix to
Euclidean quantum field theory, by K.~Symanzik, in
Local Quantum Theory, Academic Press, 1969). This is established anew here by a completely different method, using the intersection local time of two independent planar Brownian motions (whose existence was established by Geman, Horowitz and Rosen,
Ann. Prob. 12, 1984) and a sequence of dyadic decompositions of the triangle $\{0<s<t\le1\}$
Comment: Later, Dynkin, Rosen, Le Gall and others have shown existence of a renormalized local time for the multiple self-intersection of arbitrary order $n$ of planar Brownian motion. A good reference is Le Gall,
École d'Été de Saint-Flour XX, Springer LNM 1527
Keywords: Brownian motion,
Local times,
Self-intersectionNature: Original proofs Retrieve article from Numdam
XIX: 29, 332-349, LNM 1123 (1985)
YOR, Marc
Compléments aux formules de Tanaka-Rosen (
Brownian motion)
Several variants of Rosen's works (
Comm. Math. Phys. 88 (1983),
Ann. Proba. 13 (1985),
Ann. Proba. 14 (1986)) are presented. They yield Tanaka-type formulae for the self-intersection local times of Brownian motion in dimension 2 and beyond, establishing again Varadhan's normalization result (Appendix to
Euclidean quantum field theory, by K.~Symanzik, in
Local Quantum Theory, Academic Press, 1969). The methods involve stochastic calculus, which was not needed in
1928Comment: Examples of further work on this subject, using stochastic calculus or not, are Werner,
Ann. I.H.P. 29 (1993) who gives many references, Khoshnevisan-Bass,
Ann. I.H.P. 29 (1993), Rosen-Yor
Ann. Proba. 19 (1991)
Keywords: Brownian motion,
Local times,
Self-intersectionNature: Original proofs Retrieve article from Numdam
XIX: 30, 350-365, LNM 1123 (1985)
YOR, Marc
Renormalisation et convergence en loi pour des temps locaux d'intersection du mouvement brownien dans ${\bf R}^3$ (
Brownian motion)
It is shown that no renormalization à la Varadhan occurs for the self-intersection local times of 3-dimensional Brownian motion; but a weaker result is established: when the point $y\in
R^3$ tends to $0$, the self-intersection local time at $y$, on the triangle $\{0<s<u\le t\},\ t\ge0$, centered and divided by $(-\log|y|)^{1/2}$, converges in law to a Brownian motion. Several variants of this theorem are established
Comment: This result was used by Le Gall in his work on fluctuations of the Wiener sausage:
Ann. Prob. 16 (1988). Many results by Rosen have the same flavour
Keywords: Brownian motion,
Local times,
Self-intersectionNature: Original Retrieve article from Numdam
XIX: 31, 366-396, LNM 1123 (1985)
LIAO, Ming
Riesz representation and duality of Markov processes Retrieve article from Numdam
XIX: 32, 397-495, LNM 1123 (1985)
AZÉMA, Jacques
Sur les fermés aléatoires Retrieve article from Numdam
XIX: 33, 496-503, LNM 1123 (1985)
CHUNG, Kai Lai
The gauge and conditional gauge theorem Retrieve article from Numdam
XIX: 34, 504-504, LNM 1123 (1985)
DALANG, Robert C.
Correction à l'article ``Sur l'arrêt optimal de processus à temps multidimensionnel continu'' (volume XVIII) Retrieve article from Numdam
