Related papers: On Shige Peng's central limit theorem

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…

Under the sublinear expectation $\mathbb{E}[\cdot]:=\sup_{\theta\in \Theta} E_\theta[\cdot]$ for a given set of linear expectations $\{E_\theta: \theta\in \Theta\}$, we establish a new law of large numbers and a new central limit theorem…

In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.

This paper introduces the notion of pseudo-independence on the sublinear expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical conditional expectation, and the relations between pseudo-independence and Peng's independence…

In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.

In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers…

In this paper, we introduce a fundamental model for independent and identically distributed sequence with model uncertainty on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels. Thanks…

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].

M-dependence is a commonly used assumption in the study of dependent sequences. In this paper, central limit theorems for m-dependent random variables under the sub-linear expectations are established based mainly on the conditions of…

Peng, S. (\cite{P08b}) proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein's method.

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…

Peng (2008)(\cite{P08b}) proved the Central Limit Theorem under a sublinear expectation: \textit{Let $(X_i)_{i\ge 1}$ be a sequence of i.i.d random variables under a sublinear expectation $\hat{\mathbf{E}}$ with…

In this work, we develop a numerical method to study the error estimates of the $\alpha$-stable central limit theorem under sublinear expectation with $\alpha \in(0,2)$, whose limit distribution can be characterized by a fully nonlinear…

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…