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Central Limit Theorems

  • Pierre Del Moral
Part of the Probability and its Applications book series (PIA)

Abstract

The central limit theorem (abbreviated CLT) is one of the most startling results in probability theory. Loosely speaking, it expresses the fact that the sums of local and small independent disturbances (with finite variances) behave asymptotically, at least as Gaussian variables. The first CLT was stated and proved for symmetric and Bernoulli independent disturbances by A. De Moivre in the 18th century (Miscellanea anaJytica supplementum, 1730). This result was extended by P.S. Laplace in 1812 to general Bernoulli trials in his celebrated treatise Théorie analytique des probabilités.

Keywords

Central Limit Theorem Empirical Process Triangular Array Centered Gaussian Process Interact Particle Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  • Pierre Del Moral
    • 1
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse, Cedex 4France

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