XXXI: 01, 1-15, LNM 1655 (1997)
WARREN, Jonathan
Branching processes, the Ray-Knight theorem, and sticky Brownian motion
Retrieve article from Numdam
XXXI: 02, 16-23, LNM 1655 (1997)
LÉANDRE, Rémi;
NORRIS, James R.
Integration by parts and Cameron-Martin formulae for the free path space of a compact Riemannian manifold Retrieve article from Numdam
XXXI: 03, 24-39, LNM 1655 (1997)
ÜSTÜNEL, Ali Süleyman;
ZAKAI, Moshe
The change of variables formula on Wiener space Retrieve article from Numdam
XXXI: 04, 40-53, LNM 1655 (1997)
MAZET, Olivier
Classification des semi-groupes de diffusion sur $\bf R$ associés à une famille de polynômes orthogonaux Retrieve article from Numdam
XXXI: 05, 54-61, LNM 1655 (1997)
FANG, Shizan;
FRANCHI, Jacques
A differentiable isomorphism between Wiener space and path group (
Malliavin's calculus)
The Itô map $I$ is known to realize a measurable isomorphism between Wiener space $W$ and the group ${\cal P}$ of paths with values in a Riemannian manifold. Here, the pullback $I^{*}$ is shown to be a diffeomorphism (in the sense of Malliavin derivatives) between the exterior algebras $\Lambda (W)$ and $\Lambda ({\cal P})$. This allows to transfer the Weitzenböck-Shigekawa identity from $\Lambda (W)$ to $\Lambda ({\cal P})$, yielding for example the de~Rham-Hodge-Kodaira decomposition on ${\cal P}$
Keywords: Wiener space,
Path group,
Brownian motion in a manifold,
Differential formsNature: Original Retrieve article from Numdam
XXXI: 06, 62-68, LNM 1655 (1997)
JACOD, Jean;
PÉREZ-ABREU, Victor
On martingales which are finite sums of independent random variables with time dependent coefficients Retrieve article from Numdam
XXXI: 07, 69-76, LNM 1655 (1997)
AZAÏS, Jean-Marc;
WSCHEBOR, Mario
Oscillation presque sûre de martingales continues Retrieve article from Numdam
XXXI: 08, 77-79, LNM 1655 (1997)
GAO, Fuqing
A note on Cramer's theorem Retrieve article from Numdam
XXXI: 09, 80-84, LNM 1655 (1997)
HE, Sheng-Wu;
WANG, Jia-Gang
The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited Retrieve article from Numdam
XXXI: 10, 85-102, LNM 1655 (1997)
CADRE, Benoît
Une preuve ``standard'' au principe d'invariance de Stoll Retrieve article from Numdam
XXXI: 11, 103-112, LNM 1655 (1997)
LE GALL, Jean-François
Marches aléatoires auto-évitantes et mesures de polymères Retrieve article from Numdam
XXXI: 12, 113-125, LNM 1655 (1997)
ELWORTHY, Kenneth David;
LI, Xu-Mei;
YOR, Marc
On the tails of the supremum and the quadratic variation of strictly local martingales (
Martingale theory)
The asymptotic tails of the current maximum and the quadratic variation of a positive continuous local martingale are compared. Applications to strict local martingales associated with transient diffusions, such as Bessel processes, and remarkable identities for Bessel functions are given
Comment: In discrete time, see the following article
3113. Related results are due to Takaoka
3313Keywords: Continuous martingales,
Local martingales,
Quadratic variation,
Maximal processNature: Original Retrieve article from Numdam
XXXI: 13, 126-135, LNM 1655 (1997)
GALTCHOUK, Leonid I.;
NOVIKOV, Alexandre A.
On Wald's equation. Discrete time case Retrieve article from Numdam
XXXI: 14, 136-167, LNM 1655 (1997)
MICLO, Laurent
Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies Retrieve article from Numdam
XXXI: 15, 168-175, LNM 1655 (1997)
DEACONU, Mǎdǎlina;
WANTZ, Sophie
Comportement des temps d'atteinte d'une diffusion fortement rentrante Retrieve article from Numdam
XXXI: 16, 176-189, LNM 1655 (1997)
ÉMERY, Michel
Closed sets supporting a continuous divergent martingale (
Martingale theory)
This note gives a characterization of all closed subsets $F$ of $
R^d$ such that, for every $F$-valued continuous martingale $X$, the limit $X_\infty$ exists in $F$ (or $
R^d$) with non-zero probability. The criterion is as follows: To each $F$ is associated a smaller closed set $F'$ obtained, roughly speaking, by chopping off all prominent parts of $F$; this map $F\mapsto F'$ is iterated, giving a decreasing sequence $(F^n)$ with limit $F^\infty$; the condition is that $F^\infty$ is empty. (If $d=2$, $F^\infty$ is also the largest closed subset of $F$ such that all connected components of its complementary are convex)
Comment: Two similar problems are discussed in
1485Keywords: Continuous martingales,
Asymptotic behaviour of processesNature: Original Retrieve article from Numdam
XXXI: 17, 190-197, LNM 1655 (1997)
KHOSHNEVISAN, Davar
Some polar sets for the Brownian sheet Retrieve article from Numdam
XXXI: 18, 198-206, LNM 1655 (1997)
MAJER, Pietro;
MANCINO, Maria Elvira
A counter-example concerning a condition of Ogawa integrability Retrieve article from Numdam
XXXI: 19, 207-215, LNM 1655 (1997)
CHIU, Yukuang
The multiplicity of stochastic processes Retrieve article from Numdam
XXXI: 20, 216-224, LNM 1655 (1997)
EISENBAUM, Nathalie
Théorèmes limites pour les temps locaux d'un processus stable symétrique (
Limit theorems)
Using Dynkin's isomorphism, a central-limit type theorem is derived for the local times of a stable symmetric process of index $\beta$ at a finite number $n$ of levels. The limiting process is expressed in terms of a fractional, $n$-dimensional Brownian sheet with Hurst index $\beta-1$. The case when $n=1$ is due to Rosen
2533, and, for Brownian local times, to Yor
1709Comment: This kind of result is now understood as a weak form of theorems à la Ray-Knight, describing the local times of a stable symmetric process: see Eisenbaum-Kaspi-Marcus-Rosen-Shi
Ann. Prob. 28 (2000) for a Ray-Knight theorem involving fractional Brownian motion. Marcus-Rosen,
Markov Processes, Gaussian Processes, and Local Times, Cambridge University Press (2006) is a general reference on the subject
Keywords: Stable processes,
Local times,
Central limit theorem,
Dynkin isomorphism,
Fractional Brownian motion,
Brownian sheetNature: Original Retrieve article from Numdam
XXXI: 21, 225-231, LNM 1655 (1997)
GOSSELIN, Pierre;
WURZBACHER, Tilmann
An Itô type isometry for loops in ${\bf R}^d$ via the Brownian bridge Retrieve article from Numdam
XXXI: 22, 232-246, LNM 1655 (1997)
JACOD, Jean
On continuous conditional Gaussian martingales and stable convergence in law Retrieve article from Numdam
XXXI: 23, 247-251, LNM 1655 (1997)
FELDMAN, Jacob;
SMORODINSKY, Meir
Simple examples of non-generating Girsanov processes Retrieve article from Numdam
XXXI: 24, 252-255, LNM 1655 (1997)
MEYER, Paul-André
Formule d'Itô généralisée pour le mouvement brownien linéaire, d'après Föllmer, Protter, Shiryaev Retrieve article from Numdam
XXXI: 25, 256-265, LNM 1655 (1997)
TAKAOKA, Koichiro
On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem (
Stochastic calculus)
Martingales involving the future minimum of a transient Bessel process are studied, and shown to satisfy a non Markovian SDE. In dimension $>3$, uniqueness in law does not hold for this SDE. This generalizes Saisho-Tanemura
Tokyo J. Math. 13 (1990)
Comment: Extended to more general diffusions in the next article
3126Keywords: Continuous martingales,
Bessel processes,
Pitman's theoremNature: Original Retrieve article from Numdam
XXXI: 26, 266-271, LNM 1655 (1997)
RAUSCHER, Bernhard
Some remarks on Pitman's theorem (
Stochastic calculus)
For certain transient diffusions $X$, local martingales which are functins of $X_t$ and the future infimum $\inf_{u\ge t}X_u$ are constructed. This extends the preceding article
3125Comment: See also chap. 12 of Yor,
Some Aspects of Brownian Motion Part~II, Birkhäuser (1997)
Keywords: Continuous martingales,
Bessel processes,
Diffusion processes,
Pitman's theoremNature: Original Retrieve article from Numdam
XXXI: 27, 272-286, LNM 1655 (1997)
PITMAN, James W.;
YOR, Marc
On the lengths of excursions of some Markov processes Retrieve article from Numdam
XXXI: 28, 287-305, LNM 1655 (1997)
PITMAN, James W.;
YOR, Marc
On the relative lengths of excursions derived from a stable subordinator Retrieve article from Numdam
XXXI: 29, 306-314, LNM 1655 (1997)
YOR, Marc
Some remarks about the joint law of Brownian motion and its supremum (
Brownian motion)
Seshadri's identity says that if $S_1$ denotes the maximum of a Brownian motion $B$ on the interval $[0,1]$, the r.v. $2S_1(S_1-B_1)$ is independent of $B_1$ and exponentially distributed. Several variants of this are obtained
Comment: See also
3320Keywords: Maximal process,
Seshadri's identityNature: Original Retrieve article from Numdam
XXXI: 30, 315-321, LNM 1655 (1997)
ESTRADE, Anne
A characterization of Markov solutions for stochastic differential equations with jumps Retrieve article from Numdam
XXXI: 31, 322-326, LNM 1655 (1997)
LÉANDRE, Rémi
Diffeomorphism of the circle and the based loop space Retrieve article from Numdam
XXXI: 32, 327-328, LNM 1655 (1997)
COQUET, François;
MÉMIN, Jean
Correction à : Vitesse de convergence en loi pour des solutions d'équations différentielles stochastiques vers une diffusion (volume~XXVIII) Retrieve article from Numdam
XXXI: 33, 329-329, LNM 1655 (1997)
RAINER, Catherine
Correction à : Projection d'une diffusion sur sa filtration lente (volume~XXX) Retrieve article from Numdam
