I: 05, 54-71, LNM 39 (1967)
FERNIQUE, Xavier
Séries de distributions aléatoires indépendantes (2 talks) (
Miscellanea)
This is part of X.~Fernique's research on random distributions (probability measures on ${\cal D}'$, and more generally on the dual space $E'$ of a nuclear LF space $E$) and their characteristic functions, which are exactly, according to Minlos' theorem, the continuous positive definite functions on $E$ assuming the value $1$ at $0$. Here it is proved that a series of independent random distributions converges a.s. if and only if the product of their characteristic functions converges pointwise to a continuous limit, and converges a.s. after centering if and only if the product of absolute values converges
Comment: See for further results
Ann. Inst. Fourier, 17-1, 1967;
Invent. Math.,
3, 1967, and
C.R. Acad. Sc.,
266, 1968 for the extension of Lévy's continuity theorem (also presented at Séminaire Bourbaki, June 1966,
311)
Keywords: Random distributions,
Minlos theoremNature: Original
Retrieve article from Numdam
IV: 02, 28-36, LNM 124 (1970)
CARTIER, Pierre
Sur certaines variables aléatoires associées au réarrangement croissant d'un échantillon (
Miscellanea)
Presentation of combinatorial results due to D.~Foata and to Cartier-Foata, which are relevant for the theory of order statistics
Comment: See Cartier-Foata,
Problèmes combinatoires de commutation et réarrangements, LN
85, 1969
Keywords: Combinatorics,
Generating functions,
Order statisticsNature: Exposition Retrieve article from Numdam
IV: 04, 47-59, LNM 124 (1970)
DACUNHA-CASTELLE, Didier
Principe de dualité pour des espaces de suites associés à une suite de variables aléatoires (
Miscellanea)
The ``duality principe'' (too technical to be stated here) is a result of L.~Schwartz on Banach spaces of type (L), i.e., consisting of sequences $(b_n)$ such that $\sum_n b_nX_n$ is bounded in probability, where $(X_n)$ is a given sequence of r.v.'s
Comment: Related to the theory of radonifying maps, then in fast progress. To be completed
Keywords: Banach spaces,
Radonifying mapsNature: Exposition Retrieve article from Numdam
V: 01, 1-16, LNM 191 (1971)
ARTZNER, Philippe
Fonctions caractéristiques et mesures planes invariantes par rotation (
Miscellanea)
A study of the class of probability measures on the line which are projections of a measure on the plane invariant by rotation
Keywords: Characteristic functionsNature: Original Retrieve article from Numdam
VII: 09, 61-76, LNM 321 (1973)
FARAUT, Jacques
Fonction brownienne sur une variété riemannienne (
Miscellanea,
Gaussian processes)
As defined originally by Lévy in the case of spheres and euclidian spaces, a Brownian motion indexed by a point of a metric space $E$ is a centered Gaussian process $(X_t)_{t\in E}$ such that $E[(X_t-X_s)^2]=d(s,t)$, the distance. In a Riemannian manifold $d$ is understood to be the geodesic distance. The results of this paper imply that Brownian motions exist on spheres and Euclidean spaces (Lévy's original result), on real hyperbolic spaces, but not on quaternionic hyperbolic spaces
Comment: This article contains joint work with K. Harzallah
Keywords: Covariance,
Riemannian manifold,
Riemannian distance,
Lévy Brownian motions,
Several parameter Brownian motionsNature: Original Retrieve article from Numdam
VII: 28, 301-318, LNM 321 (1973)
WALDENFELS, Wilhelm von
Some remarks on Burkhardt's model for pressure broadening of spectral lines (
Miscellanea)
A model proposed by Burkhardt in 1940 for the deformation of the radiation emitted by an atom due to the surrounding atoms is transformed into probabilistic language and exactly solved
Nature: Original Retrieve article from Numdam
VIII: 08, 78-79, LNM 381 (1974)
FERNIQUE, Xavier
Une démonstration simple du théorème de R.M.~Dudley et M.~Kanter sur les lois 0-1 pour les mesures stables (
Miscellanea)
The theorem concerns stable laws on a linear space, and asserts that every measurable linear subspace has probability 0 or 1. The title describes accurately the paper
Keywords: Stable measuresNature: Original Retrieve article from Numdam
VIII: 20, 344-354, LNM 381 (1974)
WALDENFELS, Wilhelm von
Taylor expansion of a Poisson measure (
Miscellanea)
To be completed
Comment: To be completed
Keywords: Poisson point processesNature: Original Retrieve article from Numdam
IX: 03, 154-205, LNM 465 (1975)
NANOPOULOS, Photius
Mesures d'information et représentation de semi-groupes associés (
Miscellanea)
Several attempts have been made to define the information content of an event on a measurable space independently from its probability. This paper develops a point of view of Kampé de Fériet-Forte,
C.R.A.S. Paris, 265A, 1969
Keywords: Information theoryNature: Original Retrieve article from Numdam
IX: 09, 246-267, LNM 465 (1975)
DACUNHA-CASTELLE, Didier
Processus et espaces de Banach invariants par réarrangement (
Miscellanea)
The first topic of this paper is the class of processes on an interval with exchangeable increments, which includes all processes with independent and stationary increments, but also the standard Brownian bridge (for several results quoted here, see Kallenberg,
Z. für W-theorie, 27, 1973). The results are applied to problems in the classification of Banach spaces, in the spirit of Dacunha-Castelle-Schreiber,
Ann. Inst. H. Poincaré, 10, 1974
Keywords: Banach spaces,
Exchangeable random variablesNature: Original Retrieve article from Numdam
IX: 10, 268-284, LNM 465 (1975)
DACUNHA-CASTELLE, Didier
Sous-espaces symétriques des espaces d'Orlicz (
Miscellanea)
Will be asked from the author
Comment: To be asked from the author. See Dacunha-Castelle-Schreiber,
Ann. Inst. H. Poincaré, 10, 1974
Keywords: Banach spacesNature: Original Retrieve article from Numdam
IX: 11, 285-293, LNM 465 (1975)
ARTZNER, Philippe
Quelques résultats de décomposabilité en algèbre linéaire et en algèbre quadratique aléatoires (
Miscellanea)
It is shown that if a random quadratic form on $
R^4$ is a.s. of rank 3 and has an absolutely continuous law, then its law is indecomposable. To prove this, it is shown that the sum of two independent planes in $
R^4$ cannot at the same time be a.s. a hyperplane and have an absolutely continuous law (with respect to the natural measure for hyperplanes)
Keywords: Independent random subspaces,
Independent quadratic formsNature: Original Retrieve article from Numdam
IX: 13, 305-317, LNM 465 (1975)
FÖLLMER, Hans
Phase transition and Martin boundary (
Miscellanea)
To be completed
Comment: To be completed
Keywords: Random fields,
Martin boundaryNature: Original Retrieve article from Numdam
IX: 38, 565-588, LNM 465 (1975)
WALDENFELS, Wilhelm von
Interval partitions and pair interactions (
Miscellanea)
To be completed
Comment: To be completed
Nature: Original Retrieve article from Numdam
X: 06, 78-85, LNM 511 (1976)
MANDREKAR, Vidyadhar
Germ-field Markov property for multiparameter processes (
Miscellanea)
The paper studies the relations between several Markov properties of a process indexed by an open set of $
R^n$
Comment: To be completed
Keywords: Several parameter Brownian motions,
Several parameter processesNature: Original Retrieve article from Numdam
XI: 01, 1-20, LNM 581 (1977)
AVANISSIAN, Vazgain
Fonctions harmoniques d'ordre infini et l'harmonicité réelle liée à l'opérateur laplacien itéré (
Potential theory,
Miscellanea)
This paper studies two classes of functions in (an open set of) $
R^n$, $n\ge1$: 1) Harmonic functions of infinite order (see Avanissian and Fernique,
Ann. Inst. Fourier, 18-2, 1968), which are $C^\infty$ functions satisfying a growth condition on their iterated laplacians, and are shown to be real analytic. 2) Infinitely differentiable functions (or distributions) similar to completely monotonic functions on the line, i.e., whose iterated laplacians are alternatively positive and negative (they were introduced by Lelong). Among the results is the fact that the second class is included in the first
Keywords: Harmonic functions,
Real analytic functions,
Completely monotonic functionsNature: Original Retrieve article from Numdam
XII: 44, 567-690, LNM 649 (1978)
NANOPOULOS, Constantin;
NOBELIS, Photis
Régularité et propriétés limites des fonctions aléatoires (
Miscellanea,
Gaussian processes)
This paper extends to the non-Gaussian case methods to study the regularity of sample paths which have proved useful in the Gaussian case, notably that of majorizing measures (to be completed)
Comment: To be completed
Keywords: Sample path regularity,
Majorizing measuresNature: Original Retrieve article from Numdam
XII: 45, 691-706, LNM 649 (1978)
FERNIQUE, Xavier
Caractérisation de processus à trajectoires majorées ou continues (
Miscellanea,
Gaussian processes)
The methods which lead the author to necessary and sufficient conditions for boundedness or continuity of stationary Gaussian processes are extended and applied to non-stationary Gaussian processes and non-Gaussian processes
Keywords: Sample path regularityNature: Original Retrieve article from Numdam
XIII: 44, 495-520, LNM 721 (1979)
BISMUT, Jean-Michel
Problèmes à frontière libre et arbres de mesures (
Miscellanea,
Markov processes)
An optimization problem is discussed, in which one is free to choose at any time among three different transition semi-groups
Keywords: Control theoryNature: Original Retrieve article from Numdam
XIII: 46, 533-547, LNM 721 (1979)
NANOPOULOS, Photius
Mesures de probabilités sur les entiers et ensembles progressions (
Miscellanea)
To be completed
Nature: Original Retrieve article from Numdam
XIII: 47, 548-556, LNM 721 (1979)
FUJISAKI, Masatoshi
On the uniqueness of optimal controls (
Miscellanea)
``In section 1 we can give simple criteria for the uniqueness of the optimal controls whose existence is proved by Ikeda-Watanabe in the completely observable case,
Osaka Math. J.,
14, 1977. In section 2 we consider the same problem in the partially observable case.'' (From the author's summary)
Keywords: Control theoryNature: Original Retrieve article from Numdam
XIII: 49, 570-573, LNM 721 (1979)
CARMONA, René
Opérateur de Schrödinger à résolvante compacte (
Miscellanea)
A sufficient condition for a Schrödinger operator $(-1/2)ėlta+V$ to have a compact resolvent is proved, using standard properties of Brownian paths
Keywords: Schrödinger operatorsNature: Original Retrieve article from Numdam
XLVI: 10, 195-205, LNM 2123 (2014)
BAILLEUL, Ismaël
Flows driven by Banach space-valued rough paths (
Miscellanea)
This article gives a quick proof of the existence of a solution to a rough differential equations by constructing directly its associated flow. Bound on the solutions, which are valid in an infinite dimensional setting, are also given
Keywords: rough pathsNature: Original
