A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1981), Arcones (1994) and others. A Berry-Ess...

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.

We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.

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 ...

Abstract In this work the $\ell_q$ -norms of points chosen uniformly at random in a centered regular simplex high dimensions are studied. Berry–Esseen bounds regime $1\leq q < \infty$ derived and complemented by non-central limit theorem together with moderate large deviations case where $q=\infty$ . An application to intersection volume an $\ell_p^n$ -ball is also carried out.

This paper develops techniques to study the asymptotic distribution of number descents in random permutations. We relax an assumption Berry-Esseen theorem Bolthausen (1982) extend theorem's scope martingale differences time-dependent variances. present its applications other combinatorial statistics as they satisfy certain recurrence relation conditions. These include inversions, signed permuta...