Accuracy of approximation in the Poisson theorem in terms of the -distance.
Additions and correction to “The bootstrap of the mean with arbitrary bootstrap sample”
Admissible functions for cones and asumptotics of infinitely divisible distributions.
An integral representation of limit laws
An integral transformation for characteristic functions
An operator for characteristic functions
Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi
Approximated maximum likelihood estimation of parameters of discrete stable family
In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...
Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion
We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising...
Approximation of Lévy-Feller diffusion by random walk.
Approximation of stochastic differential equations driven by α-stable Lévy motion
In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer simulations....
Are squared Bessel bridges infinitely divisible
Asymptotic behaviour of stochastic systems with conditionally exponential decay property
A new class of CED systems, providing insight into behaviour of physical disordered materials, is introduced. It includes systems in which the conditionally exponential decay property can be attached to each entity. A limit theorem for the normalized minimum of a CED system is proved. Employing different stable schemes the universal characteristics of the behaviour of such systems are derived.
Atomes et lois indéfiniment divisibles dans un espace vectoriel
Band copulas as spectral measures for two-dimensional stable random vectors
In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.
Bilinear random integrals [Book]
Bochner's theorem for finite-dimensional conelike semigroups.
Calcul pratique de la distance de Prokhorov
Chaotic behavior of infinitely divisible processes
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Characterization of probability distributions by Poincaré-type inequalities