Convergence in L <sub>p</sub> Norm

James Davidson

in Stochastic Limit Theory

Published in print October 1994 | ISBN: 9780198774037
Published online November 2003 | e-ISBN: 9780191596117 | DOI:

Series: Advanced Texts in Econometrics

 Convergence in L p Norm

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This chapter looks in detail at proofs of the weak law of large numbers (convergence in probability) using the technique of establishing convergence in LP ‐norm. The extension to a proof of almost‐sure convergence is given, and then special results for martingale differences, mixingales, and approximable processes. These results are proved in array notation to allow very general forms of heterogeneity.

Keywords: approximable processes; convergence in LP‐norm; martingale differences; method of subsequences; mixingales; strong law of large numbers; weak law of large numbers

Chapter.  7291 words. 

Subjects: Econometrics and Mathematical Economics

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