The asymptotic behaviour of a closed BCMP network, with n queues and m n clients, is analyzed when n and m n become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We construct critical sequences m 0 n , which are necessary and suucient to distinguish between saturated and non-saturated regimes for the network. Several application...

We obtain a sharp estimate of the speed convergence in Boolean central limit theorem for measures with finite sixth moment. The main tool is quantitative version Stieltjes-Perron inversion formula.

Berry Esseen type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random permutation has either the uniform distribution or one which is constant over permutations with the same cycle type and having no fixed points. The size biasing bounds ...

This paper proves a Berry–Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n) as n→∞, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n) is not known even under an exponential strong mixing ...

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical ...