Chapter

Uniform 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/10.1093/0198774036.003.0021

Series: Advanced Texts in Econometrics

 Uniform Stochastic Convergence

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This chapter concerns random sequences of functions on metric spaces. The main issue is the distinction between convergence at all points of the space (pointwise) and uniform convergence, where limit points are also taken into account. The role of the stochastic equicontinuity property is highlighted. Generic uniform convergence conditions are given and linked to the question of uniform laws of large numbers.

Keywords: analytic set; Glivenko‐Cantelli theorem; pointwise convergence; stochastic equicontinuity; uniform convergence; uniform law of large numbers

Chapter.  9949 words. 

Subjects: Econometrics and Mathematical Economics

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