A Characterization of the Banach Spaces of Type p by Lévy Measures.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A note on the conditional expectations
A Note on the Product of Random Elements of a Semigroup.
A projective central limit theorem and interacting Fock space representation for the limit process
Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.
Alternative axioms for statistical physical theories
An algebra associated with the generalized sublaplacian
Boolean powers and stochastic spaces
Brownian motion, approximation of functions, and Fourier analysis
Champs markoviens et mesures de Gibbs sur
Class of unimodal distributions and its transformations
Coanalytic sets that are not Blackwell spaces
Conditional states and joint distributions on MV-algebras
In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.
Contractions on probabilistic metric spaces: examples and counterexamples.
The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,tW) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger spaces under...
Convergence in r-Mean of Normalized Partial Sums in a Separable Banach Space.
Définition et lois de probabilité des répartitions ponctuelles aléatoires
Démonstration probabiliste du théorème de d'Alembert
Didactical note: probabilistic conditionality in a Boolean algebra.
This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...
Diffusions à coefficients continus, d'après Stroock et Varadhan
Entropie, paramètres thermodynamiques, information associée aux événements et aux expériences