Chapter

Stochastic Convergence

James Davidson

in Stochastic Limit Theory

Published in print October 1994 | ISBN: 9780198774037
Published online November 2003 | e-ISBN: 9780191596117 | DOI: http://dx.doi.org/10.1093/0198774036.003.0018

Series: Advanced Texts in Econometrics

 Stochastic Convergence

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The modes of convergence introduced in Ch. 12 are studied in detail. Conditions for almost‐sure convergence are derived via the Borel‐Cantelli lemma. Convergence in probability is contrasted, and then a number of results for convergence of transformed series are given. Convergence in LP ‐norm is introduced as a sufficient condition for convergence in probability. Examples are given, and the chapter concludes with a preliminary look at the laws of large numbers.

Keywords: almost‐sure convergence; Borel's normal number theorem; Borel‐Cantelli lemma; convergence in LP‐norm; convergence in mean square; convergence in probability; law of large numbers; Slutsky's theorem

Chapter.  7163 words. 

Subjects: Econometrics and Mathematical Economics

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