Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

Rong Hu,Qunying Wu,Fabio Tramontana

doi:10.1155/2021/5526609

Rong Hu, Qunying Wu + Show 1 more

Open Access

https://doi.org/10.1155/2021/5526609

Copy DOI

Abstract

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

Highlights

In the study of probability theory and mathematical statistics, limit theory is an important research topic, which is widely used in the financial sector and other fields
The establishment of the classical limit theory requires strict conditions for the certainty model, especially in the practice of financial statistics and financial risk measurement, so its limitations are gradually highlighted by many uncertainties
Feng et al [8] obtain a complete convergence of the weighted sum of negatively dependent (ND) sequences in the sublinear expectations’ space

Summary

Introduction

In the study of probability theory and mathematical statistics, limit theory is an important research topic, which is widely used in the financial sector and other fields. Feng et al [8] obtain a complete convergence of the weighted sum of negatively dependent (ND) sequences in the sublinear expectations’ space. Liang and Wu [11] research on complete convergence and complete integral convergence for extended negatively dependent (END) random variables under sublinear expectations. Complete convergence has been studied very deeply in probability space, for example, Liang and Su [13] obtain the complete convergence theorem for weighted sums of negatively associated (NA) sequences and discuss its necessity. We establish the complete convergence theorem for weighted sums of widely acceptable (WA) random variables under sublinear expectations. Let 􏼈Yn, n ≥ 1􏼉 be a sequence of random variables in a sublinear expectation space(Ω, H, E^). It is obvious that if 􏼈Xn; n ≥ 1􏼉 is a sequence of widely acceptable random variables and functions f1(x), f2(x), .

Lemma random

It is easily checked that

Similar to