Suppose Xi, i = 1,2,... are i.i.d. positive random variables with d.f. F. We assume the tail d.f. F̄ = 1 - F to be regularly varying (F̄(tx)|F̄(t) → x-β,x > 0,t → ∞) with 0 x) as x → ∞ where SN = ΣN 1 Xi and N,Xi(i≥ 1) independent with Σ∞ n=0P(N = n)xn analytic at x = 1 is studied under an additional smoothness condition on F. As an application we give the asymptotic behaviour of the expected population size of an age-dependent branching process
Let G = [Sigma][infinity]n=0pnF*n denote the probability measure subordinate to F with subordinator ...
24 pagesInternational audienceWe consider sequences of random variables of the type $S_n= n^{-1/2} \...
AbstractA martingale, previously used to prove the classical almost sure convergence of the normed s...
AbstractSuppose Xi, i = 1, 2, … are i.i.d. positive random variables with d.f. F. We assume the tail...
Suppose Xi, I = 1, 2, ... are i.i.d. positive random variables with d.f. F. We assume the tail d.f. ...
AbstractLet G = Σ∞n=0pnF∗n denote the probability measure subordinate to F with subordinator {Pn}N. ...
AbstractSuppose G is a distribution function on [0, ∞) and F(x)=∑∞n=0pnG(n)(x)We prove necessary and...
AbstractLet X1, X2,… be i.i.d. random variables with continuous distribution function F < 1. It is k...
AbstractIn proving limit theorems for some stochastic processes, the following classes of distributi...
Motivated by a seminal paper of Kesten et al. (Ann. Probab., 3(1), 1–31, 1975) we consider a branchi...
AbstractIt is shown that any real-valued sequence of random variables {Xn} converging in probability...
AbstractLet (Z(t):t⩾0) be a supercritical age-dependent branching process and let {Yn} be the natura...
AbstractIn R2 the integral of a regularly varying (RV) function f is regularly varying only if f is ...
In this paper we show for a large class of heavy tailed random variables a second order asymptotic r...
AbstractLet Z(t) be the population at time t of a critical age-dependent branching process. Suppose ...
Let G = [Sigma][infinity]n=0pnF*n denote the probability measure subordinate to F with subordinator ...
24 pagesInternational audienceWe consider sequences of random variables of the type $S_n= n^{-1/2} \...
AbstractA martingale, previously used to prove the classical almost sure convergence of the normed s...
AbstractSuppose Xi, i = 1, 2, … are i.i.d. positive random variables with d.f. F. We assume the tail...
Suppose Xi, I = 1, 2, ... are i.i.d. positive random variables with d.f. F. We assume the tail d.f. ...
AbstractLet G = Σ∞n=0pnF∗n denote the probability measure subordinate to F with subordinator {Pn}N. ...
AbstractSuppose G is a distribution function on [0, ∞) and F(x)=∑∞n=0pnG(n)(x)We prove necessary and...
AbstractLet X1, X2,… be i.i.d. random variables with continuous distribution function F < 1. It is k...
AbstractIn proving limit theorems for some stochastic processes, the following classes of distributi...
Motivated by a seminal paper of Kesten et al. (Ann. Probab., 3(1), 1–31, 1975) we consider a branchi...
AbstractIt is shown that any real-valued sequence of random variables {Xn} converging in probability...
AbstractLet (Z(t):t⩾0) be a supercritical age-dependent branching process and let {Yn} be the natura...
AbstractIn R2 the integral of a regularly varying (RV) function f is regularly varying only if f is ...
In this paper we show for a large class of heavy tailed random variables a second order asymptotic r...
AbstractLet Z(t) be the population at time t of a critical age-dependent branching process. Suppose ...
Let G = [Sigma][infinity]n=0pnF*n denote the probability measure subordinate to F with subordinator ...
24 pagesInternational audienceWe consider sequences of random variables of the type $S_n= n^{-1/2} \...
AbstractA martingale, previously used to prove the classical almost sure convergence of the normed s...
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