Sulla assoluta continuità di una variabile aleatoria la cui densità è limite di una successione di densità costanti a tratti
Sur la répartition des suites de Kakutani (I)
Sur la répartition des suites de Kakutani (II)
Sur le jeu de Saint-Pétersbourg
Sur le théorème en moyenne d'Akcoglu-Sucheston.
Sur les solutions d'une équation fonctionnelle non linéaire de B. Mandelbrot
Sur une extension de la notion de loi semi-stable
Survival probabilities of autoregressive processes
Given an autoregressive process X of order p (i.e. Xn = a1Xn−1 + ··· + apXn−p + Yn where the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending on the coefficients a1,..., ap and the distribution of Y1, we state conditions under which the survival probability decays polynomially, faster than polynomially or converges to a positive constant....
-law of large numbers for fuzzy numbers
The notions of a -norm and of a fuzzy number are recalled. The law of large numbers for fuzzy numbers is defined. The fuzzy numbers, for which the law of large numbers holds, are investigated. The case when the law of large numbers is violated is studied.
Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable
We give a sufficient condition for a non-negative random variable to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler’s complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution...
The analytic fixed point function. II.
The Barnes G function and its relations with sums and products of generalized gamma convolution variables.
The Beurling estimate for a class of random walks.
The convergence of sums of transition probabilities of a positive recurrent Markov chain.
The distribution of divisors of N!
The effect of random scale changes on limits of infinitesimal systems.
The Hawkins sieve and brownian motion
The intersections of random finite sets
The principle of truncations in applied probability
Théorèmes limite quotient pour chaînes de Markov récurrentes au sens de Harris