Chapter

Weak Convergence in a Function Space

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/10.1093/0198774036.003.0027

Series: Advanced Texts in Econometrics

 Weak Convergence in a Function Space

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This chapter applies the theory of Ch. 26 to the case of the space C of continuous functions on the unit interval. It is shown how to assign probability measures to C, and Weiner measure (Brownian motion) and a number of related Gaussian cases are exhibited as examples. Weak convergence on C is discussed, and a functional CLT (a version of Donsker's theorem for martingales) is given. The multivariate generalization of the FCLT is also given.

Keywords: Brownian motion; consistency properties; coordinate projections; Donsker's theorem; finite dimensional distributions; function spaces; functional central limit theorem; space C; weak convergence; Wiener measure

Chapter.  12291 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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