The relevation transform and a generalization of the gamma distribution function
The Reverse Isoperimetric Problem for Gaussian Measure.
The role of functional equations in stochastic model building.
The space of distribution functions is separable.
The space of distribution functions endowed with the metric introduced in [5] is separable.
The strong law of large numbers for -statistics with dependent data.
The use of fractional calculus in probability
The -deformation of the classical convolution
We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by . We deal with the -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the -deformed classical convolution and give the orthogonal polynomials...
The variogram and estimation error in connection with the assessment of continuous streams.
Théorème de convergence vers des lois stables pour une classe de chaînes de Markov
Theory of classification : a survey of some recent advances
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Theory of Classification: a Survey of Some Recent Advances
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Thin-shell concentration for convex measures
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.
Threshold phenomena on product spaces: BKKKL revisited (once more).
Toward the best constant factor for the Rademacher-Gaussian tail comparison
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c1 and c2 such that c2≈1.01 c1. A discussion of relative merits of this result versus limit theorems is given.
Transformations groups of the Andersson-Perlman cone.
Transformations of copulas
Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.
Transportation approach to some concentration inequalities in product spaces.
Transportation inequalities for stochastic differential equations of pure jumps
For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...
Trends to equilibrium in total variation distance
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling us to study our problem firstly via usual functional inequalities (Poincaré inequality, weak Poincaré,…) and truncation procedure, and secondly through the introduction of new functional inequalities ....