An integral representation of limit laws
An integral transformation for characteristic functions
An Introduction to the Theory of Stochastic Orders.
An isoperimetric inequality on the ℓp balls
The normalised volume measure on the ℓnp unit ball (1≤p≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pãlog1−1/p(1/ã), where ã=min(a, 1−a).
An observation about submatrices.
An operator for characteristic functions
Analytic and Asymptotic Properties of Non-Symmetric Linnik's Probability Densities.
Angles de droits et de revers. Distribution circulaire
Dans cet article, on traite un échantillon d'angles de droits et de revers de pièces de monnaies. On a cherché à en donner une description statistique correcte et à ajuster une loi théorique puis à construire un test d'homogénéité non paramétrique de deux échantillons distribués sur le cercle.
Application des lois non paramétriques dans les systèmes d’attente et la théorie de renouvellement
Les distributions non paramétriques de survie trouvent, de plus en plus, des applications dans des domaines très variés, à savoir : théorie de fiabilité et analyse de survie, files d’attente, maintenance, gestion de stock, théorie de l’économie, L’objet de ce travail est d’utiliser les bornes inférieures et supérieures (en terme de la moyenne) des fonctions de fiabilité appartenant aux classes de distribution de type et , présentées par Sengupta (1994), pour l’évaluation de certaines caractéristiques....
Application des lois non paramétriques dans les systèmes d'attente et la théorie de renouvellement
Les distributions non paramétriques de survie trouvent, de plus en plus, des applications dans des domaines très variés, à savoir: théorie de fiabilité et analyse de survie, files d'attente, maintenance, gestion de stock, théorie de l'économie, ... L'objet de ce travail est d'utiliser les bornes inférieures et supérieures (en terme de la moyenne) des fonctions de fiabilité appartenant aux classes de distribution de type IFR, DFR, NBU et NWU, présentées par Sengupta (1994), pour l'évaluation de...
Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi
Applications of an Inequality Involving Conditional Expectations.
Applications of monotonic dependence functions: descriptive aspects
Approximate Distributions of Order Statistics, with Applications to Nonparametric Statistics - R. D. Reiss.
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 continuous mappings preserving normality necessarily linear?
An example of a normal nonlinear continuous function of a normal random variable is given. Also the Cauchy case is considered.
Are law-invariant risk functions concave on distributions?
While it is reasonable to assume that convex combinations on the level of random variables lead to a reduction of risk (diversification effect), this is no more true on the level of distributions. In the latter case, taking convex combinations corresponds to adding a risk factor. Hence, whereas asking for convexity of risk functions defined on random variables makes sense, convexity is not a good property to require on risk functions defined on distributions. In this paper we study the interplay...