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<p>We first provide a biosketch of Doob, Feller, and Stein, then describe the foundational works of Doob and Feller in mathematical probability, establishing probability as an essential part of mathematics. We then sketch Stein’s Method, which spurs the modern developments in deriving convergence and rates of convergence in general situations, way beyond the classical iid case. Recent developments in Statistical and Quantum Physics, Biomedicine, and Engineering in 21st Century Probability are given in the last section.</p>

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From Doob and Feller to Stein’s Method and Back

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Kwok Pui Choi,
  • Tze Leung Lai

摘要

We first provide a biosketch of Doob, Feller, and Stein, then describe the foundational works of Doob and Feller in mathematical probability, establishing probability as an essential part of mathematics. We then sketch Stein’s Method, which spurs the modern developments in deriving convergence and rates of convergence in general situations, way beyond the classical iid case. Recent developments in Statistical and Quantum Physics, Biomedicine, and Engineering in 21st Century Probability are given in the last section.