相关论文: Marcinkiewicz-Zygmund and ordinary strong laws for…

We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…

In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach…

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…

Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when $\pi$ is heavy-tailed. Constructing a (random)…

This note develops Rio's proof [C. R. Math. Acad. Sci. Paris, 1995] of the rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers to the case of sums of dependent random variables with regularly varying normalizing…

The weak and strong laws of large numbers for time-inhomogeneous Markov chains are studied under general conditions. First, under Drift Condition and Contraction Condition in total variation, we prove the weak law of large numbers. Then,…

The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…

We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using the nonparametric maximum likelihood based plug-in estimator. We find the exact asymptotic distribution of…

We consider two nonparametric estimators for the risk measure of the sum of $n$ i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order $n$. This framework…

The Strong Law of Large Numbers (SLLN) for random variables or random vectors with different mathematical expectations easily reduces by means of shifts to SLLN for random variables or random vectors whose mathematical expectations are…

This paper presents GMM and M estimators and their asymptotic properties for network-dependent data. To this end, I build on Kojevnikov, Marmer, and Song (KMS, 2021) and develop a novel uniform law of large numbers (ULLN), which is…

This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…

Using the approach of N. Etemadi for the Strong Law of Large Numbers (SLLN) from 1981 and the elaboration of this approach by S. Cs\"org\H{o}, K. Tandori and V. Totik from 1983, I give weak conditions under which the SLLN still holds for…

We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic)…

We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…

Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism -\beta(x) z+\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy). The skeleton decomposition provides a pathwise description of the process…

We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930],…

This article studies the asymptotic behaviors of nonparametric estimators of two overlapping measures, namely Pianka's and MacArthur-Levins measures. The plug-in principle and the method of kernel density estimation are used to estimate…

The Marcinkiewicz Strong Law, $\displaystyle\lim_{n\to\infty}\frac{1}{n^{\frac1p}}\sum_{k=1}^n (D_{k}- D)=0$ a.s. with $p\in(1,2)$, is studied for outer products $D_k=X_k\overline{X}_k^T$, where $\{X_k\},\{\overline{X}_k\}$ are both…