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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Stochastic Convergence

Stochastic Convergence

(p.281) 18 Stochastic Convergence
Stochastic Limit Theory

James Davidson

Oxford University Press

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

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