Scholarlink

Abstract <p> In a recent study [Ann. Probab. 47 (4) 2172–2185, 2019], M. Fathi obtained new rates of convergence in the central limit theorem for the log-concave situations. His approach is based on analyzing Stein kernels using moment maps. In the present paper, we replace moment maps by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-moment maps and describe construction of Stein kernels using <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-moment maps, which are convex solutions of a Monge–Ampère equation in [Nonlinear Anal. 239 (2024), 113417]. Then a bound on the Kantorovich–Wasserstein distance in the central limit theorem and in the context of probability distributions of negative powers is proved. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

\(q\)-Moment Stein Kernels: Application to the Rate of Convergence in the Multidimensional CLT

  • 期刊论文

  • 发表日期：

    2025年10月1日

查看全文
  • H. Khanh

摘要

Abstract

In a recent study [Ann. Probab. 47 (4) 2172–2185, 2019], M. Fathi obtained new rates of convergence in the central limit theorem for the log-concave situations. His approach is based on analyzing Stein kernels using moment maps. In the present paper, we replace moment maps by \(q\) -moment maps and describe construction of Stein kernels using \(q\) -moment maps, which are convex solutions of a Monge–Ampère equation in [Nonlinear Anal. 239 (2024), 113417]. Then a bound on the Kantorovich–Wasserstein distance in the central limit theorem and in the context of probability distributions of negative powers is proved.