Weak Convergence of Distributions

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

 Weak Convergence of Distributions

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This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved, and the chapter then considers the preservation of weak convergence under transformations. Next, the role of moments and characteristic functions is considered, and lastly, criteria for weak convergence and the leading case of random sums.

Keywords: characteristic function; continuous mapping theorem; Helly's selection theorem; infinitely divisible distribution; Lévy continuity theorem; Skorokhod representation theorem; stable distribution; uniform tightness; weak convergence

Chapter.  8767 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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