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Inequalities for independent random vectors under sublinear expectations

Xiaojuan Li, Mingshang Hu

Abstract

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.

Inequalities for independent random vectors under sublinear expectations

Abstract

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.

Paper Structure

This paper contains 3 sections, 5 theorems, 25 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main results

Key Result

Theorem 2.1

There exists a convex and weakly compact set of probability measures $\mathcal{P}$ on $(\Omega,\mathcal{B}(\Omega))$ such that where $\mathcal{B}(\Omega)$ is the Borel $\sigma$-field.

Theorems & Definitions (7)

  • Theorem 2.1
  • Definition 2.2
  • Proposition 2.3
  • Theorem 3.1
  • Theorem 3.2
  • Remark 3.3
  • Theorem 3.4