Related papers: Stein's Method for Law of Large Numbers under Subl…
We consider random operators $\Omega \to \mathcal{L}(\ell_p, \ell_p)$ for some $1 \leqslant p < \infty$. The law of large numbers is known in the case $p=2$ in the form of usual law of large numbers. Instead of sum of i.i.d. variables there…
Three versions of the Weak Law of Large Numbers are proposed for weakly dependent and generally speaking non-equally distributed random variables, with finite or possibly infinite expectations.
In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…
We derive a simple proof, based on information theoretic inequalities, of an upper bound on the largest rates of $q$-ary $\overline{2}$-separable codes that improves recent results of Wang for any $q\geq 13$. For the case $q=2$, we recover…
In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to…
The results of the study provide guidelines for the development and applications of algorithms. When the number of steps for calculating an assumption tends to infinity, probability theory can be applied to predict whether the assumption…
The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…
The aim of this paper is to establish the Marcinkiewicz-Zygmund (MZ) type law of large numbers for the randomly weighted sums with weights chosen randomly, uniformly over the unit sphere in $\mathbb{R}^n$. We also establish a theorem that…
For $\alpha\in (1,2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential…
The Eulerian number A(n,k) counts permutations of n symbols with exactly k descents. Motivated by problems in cryptography, several authors have studied the proportion of permutations whose number of descents lies in a fixed congruence…
We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…
Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…
Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions…
This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…
We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).
We establish a law of large numbers for a certain class of vector-valued linear statistics for the Bergman determinantal point process on the unit disk. Our result seems to be the first LLN for vector-valued linear statistics in the setting…
We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent non-identically distributed random variables. These results generalize Etemadi's extension of…
We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for…