Related papers: A central limit theorem under sublinear expectatio…
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, 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.
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…
In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
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…
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)…
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…
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…
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…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
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…
In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under…
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…
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…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
In this paper, with the notion of independent identically distributed (IID) random variables under sublinear expectations introduced by Peng [7-9], we investigate moment bounds for IID sequences under sublinear expectations. We can obtain a…
We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.