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Two basic limit theorems regarding weak convergence are studied. The first one is the Central Limit Theorem (CLT) under the general Lindeberg condition, which explains why the Gaussian distribution plays such a prominent role in probability and statistics. The second one is the Limit Theorem of Poisson, which shows accordingly the natural role of the Poisson distribution. Finally, the speed of convergence of the CLT is investigated by the Berry-Esseen theorem and Stein’s method.

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Limit Theorems for Weak Convergence

  • 章节

  • 发表日期：

    2025年

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  • Hannah Geiss,
  • Stefan Geiss

摘要

Two basic limit theorems regarding weak convergence are studied. The first one is the Central Limit Theorem (CLT) under the general Lindeberg condition, which explains why the Gaussian distribution plays such a prominent role in probability and statistics. The second one is the Limit Theorem of Poisson, which shows accordingly the natural role of the Poisson distribution. Finally, the speed of convergence of the CLT is investigated by the Berry-Esseen theorem and Stein’s method.