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<p>In this paper, the authors firstly establish the weak laws of large numbers on the canonical space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11401_2025_7_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\((\mathbb{R}^{\mathbb{N}},\cal{B}(\mathbb{R}^{\mathbb{N}}))\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mrow> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msup> <mo>,</mo> <mrow> <mi mathvariant="script">B</mi> </mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mrow> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Xinpeng Li,
  • Gaofeng Zong

摘要

In this paper, the authors firstly establish the weak laws of large numbers on the canonical space \((\mathbb{R}^{\mathbb{N}},\cal{B}(\mathbb{R}^{\mathbb{N}}))\) ( R N , B ( R 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.