This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein’s method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integral...

We study the convergence rate to normal limit law for the space requirement of random m-ary search trees. While it is known that the random variable is asymptotically normally distributed for 3 ≤ m ≤ 26 and that the limit law does not exist for m > 26, we show that the convergence rate is O(n) for 3 ≤ m ≤ 19 and is O(n), where 4/3 < α < 3/2 is a parameter depending on m for 20 ≤ m ≤ 26. Our app...

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 ...

A central limit theorem and a moderate deviations principle for the ratio of geometric p-generalized arithmetic mean are shown. Also Berry–Esseen-type upper bound on rate convergence in is proved. This has implications probabilistic version question whether inequality between can be reversed or improved up to multiplicative constants. The involved random vectors we study belong class distributi...

The central limit theorem is considered with respect to the transport distance W2. We discuss an alternative approach to a result of E. Rio, based on a Berry–Esseen-type bound for the entropic distance to the normal distribution. © 2013 Elsevier B.V. All rights reserved. Let X and Z be random variables with distributions F and G, having finite second moments. The Kantorovich distance W2(F ,G) b...

We consider state-dependent channels with general state available at both the encoder and the decoder. We establish the "-capacity and the optimistic "-capacity of such channels. The determination of these capacities allows us to provide a necessary and sufficient condition for the strong converse property to hold. We also provide a simpler sufficient condition on the firstand second-order stat...