Entropy considerations in the noncommutative setting.
Equivalent-singular dichotomy for quasi-invariant ergodic measures
Estimates of Hellinger integrals of infinitely divisible distributions
Estimation of parameters of a spherical invariant stable distribution
This paper concerns the estimation of the parameters that describe spherical invariant stable distributions: the index α ∈ (0,2] and the scale parameter σ >0. We present a kind of moment estimators derived from specially transformed original data.
Exact rates of convergence to the local times of symmetric Lévy processes
Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in with non-zero mean.
Existence theorems for measures on continous posets, with applications to random set theory.
Factors and Roots of Large Measures on Connected Lie Groups.
Fractional flux and non-normal diffusion.
Free generalized gamma convolutions.
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a...
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we...
Generalized Bell polynomials and the combinatorics of Poisson central moments.
Generalized convolutions IV
Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples.
Generalized Levy representation of norms and isometric embeddings into -spaces
Generalized tempered stable processes
This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy processes are...
Geometric infinite divisibility, stability, and self-similarity: an overview
The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of components for each p ∈ (0,1), where is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....
Geometric Stable Laws Through Series Representations
Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic...
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.