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Marcinkiewicz-type laws of large numbers for pseudo-independent random variables under sublinear expectations

Jialiang Fu

Abstract

As a kind of independence of random variables under sublinear expectations, pseudo-independence is weaker than Peng's independence. We shall give Marcinkiewicz-type weak and strong laws of large numbers for pseudo-independent random variables under the framework of sublinear expectations.

Marcinkiewicz-type laws of large numbers for pseudo-independent random variables under sublinear expectations

Abstract

As a kind of independence of random variables under sublinear expectations, pseudo-independence is weaker than Peng's independence. We shall give Marcinkiewicz-type weak and strong laws of large numbers for pseudo-independent random variables under the framework of sublinear expectations.
Paper Structure (6 sections, 5 theorems, 66 equations)

This paper contains 6 sections, 5 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main results
  4. Proofs
  5. Marcinkiewicz-type weak law of large numbers
  6. Marcinkiewicz-type strong law of large numbers

Key Result

Proposition 2.1

An independent sequence of random variables $\{X_n,n\geq1\}$ on $(\Omega,\mathcal{F},\widehat{\mathbb{E}})$ is pseudo-independent.

Theorems & Definitions (12)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • Proposition 2.1
  • Remark 2.2
  • Theorem 2.1
  • Theorem 3.1
  • Theorem 3.2
  • Corollary 3.1
  • ...and 2 more