New viewpoints, results and problems in the theory of Phragmén-Lindelöf
No return to convexity
We study the closures of classes of log-concave measures under taking weak limits, linear transformations and tensor products. We investigate which uniform measures on convex bodies can be obtained starting from some class 𝒦. In particular we prove that if one starts from one-dimensional log-concave measures, one obtains no non-trivial uniform mesures on convex bodies.
Noncommutative extensions of the Fourier transform and its logarithm
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗ ν̂ ∘ Δ when...
Non-commutative probability limit theorems
Non-Exponential Families of Distributions.
Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities.
We study the law of functionals whose prototype is ∫0+∞ eBs(ν) dWs(μ),where B(ν) and W(μ) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of in variant diffusions on the hyperbolic half-plane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic half-plane and Bessel processes).
Note on dispersion of .
Note on Dispersion of Xalpha
Note on the multidimensional Gebelein inequality
We generalize the Gebelein inequality for Gaussian random vectors in .
Note on the variance of the sum of Gaussian functionals
Let be a Gaussian sequence with for each i and suppose its correlation matrix is the matrix of some linear operator R:l₂→ l₂. Then for , i=1,2,..., where μ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals , i=1,2,... .
Note on type II counter problem
In the paper the authors investigate the explicit form of the joint Laplace transform of the distances between two subsequent moments f particle registrations by the Type II counter (the counter with prolonged dead time), in the general case, and the generating function of the number of particles arriving during the dead time. They give explicit solutions to the complicated integral equations obtained by L. Takács and R. Pyke, respectively. Moreover, they study the geometric behaviour of the distribution...
Note sur quelques inégalités entre les valeurs probables d'une grandeur aléatoire qui ne prend que des valeurs positives
Note sur une loi de probabilité discrète méconnue
Notes on Qi type integral inequalities.
Number of representations related to a linear recurrent basis
On a characterization of symmetric stable processes.
On a characterization of symmetric stable processes. (Short Communication).
On a Class of Discrete Distributions Arising from the Birth-Death-with-Immigration Process.
On a class of perimeter-type distances of probability distributions
On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions.