Applying Stein's method, an inductive technique and size bias coupling yields a Berry–Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of vertices in the Erd˝ os–Rényi random graph of a given degree. 1. Introduction. We present a new Berry–Esseen theorem for sums Y of dependent variables by combinin...

We study the rate of convergence in central limit theorem for Euclidean norm random orthogonal projections vectors chosen at from an $\ell _p^n$-ball which has been obtained [D. Alonso-Gutiérrez et al., Bernoulli 25 (2019)]. More p

Abstract We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation dual and the mean width polyhedral sets are obtained. deduce these results by proving a general theorem weighted volume convex hull points chosen from boundary smooth body according to positive continuous density Euclide...

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate via certain Monte Carlo simulations. main results represent upper bound errors between exact solution and approximation, estimate fluctuation appropriate central limit theorem (CLT) construction confidence intervals. Moreover, provide rates convergence ...

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends not only geometric features the underlying but also modified harmonic embedding graph into certain nilpotent Lie group. Moreover, we apply rate convergence Trotter's approximation theorem to establish...