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 sufficient to distinguish between saturated and non-saturated regimes for the network. Several applicati...

Abstract In this article, we take a probabilistic look at Hölder's inequality, considering the ratio of terms in classical Hölder inequality for random vectors . We prove central limit theorem ratio, which then allows us to reverse up multiplicative constant with high probability. The models randomness include uniform distribution on balls and spheres. also provide Berry–Esseen–type result larg...

We prove a Berry–Esseen theorem and Edgeworth expansions for partial sums of the form $$\displaystyle S_N=\sum \nolimits _{n=1}^{N}f_n(X_n,X_{n+1})$$ , where $$\{X_n\}$$ is uniformly elliptic inhomogeneous Markov chain $$\{f_n\}$$ sequence bounded functions. The holds without additional assumptions, while order 1 hold when irreducible, which an optimal condition. For higher expansions, we then ...

Let Z:={Zt,t≥0} be a stationary Gaussian process. We study two estimators of E[Z02], namely fˆT(Z):=1 T ∫0TZt2dt, and f˜n(Z):=1 n ∑i=1nZti2, where ti=iΔn, i=0,1,…,n, Δn→0 Tn:=nΔn→∞. prove that the are strongly consistent establish Berry-Esseen bounds for central limit theorem involving fˆT(Z) f˜n(Z). apply these results to asymptotically processes estimate drift parameter Ornstein-Uhlenbeck pro...