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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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Weak Convergence in a Function Space

Weak Convergence in a Function Space

(p.434) 27 Weak Convergence in a Function Space
Stochastic Limit Theory

James Davidson

Oxford University Press

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

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