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XXXI: 01, 1-15, LNM 1655 (1997)
WARREN, Jonathan
Branching processes, the Ray-Knight theorem, and sticky Brownian motion
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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
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XXXI: 03, 24-39, LNM 1655 (1997)
ÜSTÜNEL, Ali Süleyman; ZAKAI, Moshe
The change of variables formula on Wiener space
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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
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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 forms
Nature: Original
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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
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XXXI: 07, 69-76, LNM 1655 (1997)
AZAÏS, Jean-Marc; WSCHEBOR, Mario
Oscillation presque sûre de martingales continues
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XXXI: 08, 77-79, LNM 1655 (1997)
GAO, Fuqing
A note on Cramer's theorem
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XXXI: 09, 80-84, LNM 1655 (1997)
HE, Sheng-Wu; WANG, Jia-Gang
The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited
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XXXI: 10, 85-102, LNM 1655 (1997)
Une preuve standard'' au principe d'invariance de Stoll
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XXXI: 11, 103-112, LNM 1655 (1997)
LE GALL, Jean-François
Marches aléatoires auto-évitantes et mesures de polymères
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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 3313
Keywords: Continuous martingales, Local martingales, Quadratic variation, Maximal process
Nature: Original
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XXXI: 13, 126-135, LNM 1655 (1997)
GALTCHOUK, Leonid I.; NOVIKOV, Alexandre A.
On Wald's equation. Discrete time case
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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
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XXXI: 15, 168-175, LNM 1655 (1997)
DEACONU, Mǎdǎlina; WANTZ, Sophie
Comportement des temps d'atteinte d'une diffusion fortement rentrante
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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 1485
Keywords: Continuous martingales, Asymptotic behaviour of processes
Nature: Original
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XXXI: 17, 190-197, LNM 1655 (1997)
KHOSHNEVISAN, Davar
Some polar sets for the Brownian sheet
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XXXI: 18, 198-206, LNM 1655 (1997)
MAJER, Pietro; MANCINO, Maria Elvira
A counter-example concerning a condition of Ogawa integrability
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XXXI: 19, 207-215, LNM 1655 (1997)
CHIU, Yukuang
The multiplicity of stochastic processes
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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 1709
Comment: 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 sheet
Nature: Original
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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
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XXXI: 22, 232-246, LNM 1655 (1997)
JACOD, Jean
On continuous conditional Gaussian martingales and stable convergence in law
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XXXI: 23, 247-251, LNM 1655 (1997)
FELDMAN, Jacob; SMORODINSKY, Meir
Simple examples of non-generating Girsanov processes
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XXXI: 24, 252-255, LNM 1655 (1997)
MEYER, Paul-André
Formule d'Itô généralisée pour le mouvement brownien linéaire, d'après Föllmer, Protter, Shiryaev
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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 3126
Keywords: Continuous martingales, Bessel processes, Pitman's theorem
Nature: Original
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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 3125
Comment: See also chap. 12 of Yor, Some Aspects of Brownian Motion Part~II, Birkhäuser (1997)
Keywords: Continuous martingales, Bessel processes, Diffusion processes, Pitman's theorem
Nature: Original
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XXXI: 27, 272-286, LNM 1655 (1997)
PITMAN, James W.; YOR, Marc
On the lengths of excursions of some Markov processes
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XXXI: 28, 287-305, LNM 1655 (1997)
PITMAN, James W.; YOR, Marc
On the relative lengths of excursions derived from a stable subordinator
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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
Nature: Original
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XXXI: 30, 315-321, LNM 1655 (1997)
A characterization of Markov solutions for stochastic differential equations with jumps
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XXXI: 31, 322-326, LNM 1655 (1997)
LÉANDRE, Rémi
Diffeomorphism of the circle and the based loop space
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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)
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XXXI: 33, 329-329, LNM 1655 (1997)
RAINER, Catherine
Correction à : Projection d'une diffusion sur sa filtration lente (volume~XXX)
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