On the Necessary and Sufficient Conditions for Peng’s Law of Large Numbers Under Sublinear Expectations

Abstract

In this paper, the authors firstly establish the weak laws of large numbers on the canonical space $(\mathbb{R}^{\mathbb{N}},\cal{B}(\mathbb{R}^{\mathbb{N}}))$ by traditional truncation method and Chebyshev’s inequality as in the classical probability theory. Then they extend them from the canonical space to the general sublinear expectation space. The necessary and sufficient conditions for Peng’s law of large numbers are obtained.

Keywords

Canonical space / Independence and identical distribution / Peng’s law of large numbers / Sublinear expectation / 60A05 / 60F05 / 60E05 / 60A86

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