Limit theorems for non-additive probabilities or non-linear expectations are challenging
issues which have attracted a lot of interest recently. The purpose of this paper is to study the …

Motivated by recently emerging problems in machine learning and statistics, we propose
data models which relax the familiar iid assumption. In essence, we seek to understand what …

Shige Peng's sublinear expectations generalize ordinary linear expectation operators. It is
shown that the behaviour of sample averages of Peng iid variables may be very different …

In this paper we study the weak laws of large numbers for sublinear expectation. We prove
that, without any moment condition, the weak laws of large numbers hold in the sense of …

In this paper, we investigate capacity preserving transformations and their ergodicity. We
obtain some limit properties under capacity spaces and then give the concept of ergodicity …

We prove by counterexample that a large deviation principle established by Chen and Feng
[{\em Comm. Statist. Theory Methods}{\bf 45}(2016), 400--412] in the framework of sublinear …

In this paper, with a new notion of exponential independence for random variables under an
upper expectation, we establish a kind of strong laws of large numbers for capacities. Our …

In this paper, we discuss a potential agenda for future work in the theory of random sets and
belief functions, touching upon a number of focal issues: the development of a fully-fledged …

A law of large numbers for the possibilistic mean value of a variable in a possibility space is
presented. An example shows that the convergence in distribution (under a definition …

The purpose of this study is to probe the transformations that preserve capacities, their
ergodicity and mixing behaviors. Firstly, definitions of different levels of mixing and ergodicity …