Weak convergence of measures: applications in probability

Patrick Billingsley9780898711769, 0898711762

A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod’s representation theorem; Prokhorov’s theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.

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Table of contents :
Weak Convergence of Measures:Applications in Probability……Page 1
Contents……Page 8
Preface……Page 10
1. Introduction…….Page 12
2. Weak convergence…….Page 13
3. Random elements and convergence in distribution…….Page 17
4. Prokhorov’s theorem…….Page 20
5. The space……Page 23
6. A maximal inequality…….Page 27
7. Tightness…….Page 31
8. Limit theorems…….Page 34
BIBLIOGRAPHY……Page 39