Anscombe's Theorem 60 Years Later

Abstract

The point of departure of the present article is Anscombe's seminal 1952 paper on limit theorems for randomly indexed processes. We discuss the importance of this result and mention some of its impact, mainly on stopped random walks. The main aim of the article is to illustrate the beauty and efficiency of what will be called the stopped random walk (SRW) method.

Keywords:

• Perturbed random walks
• Random index
• Random sum central limit theorem
• Random walk
• Records
• Renewal theory
• Repeated significance test
• Sequential analysis
• SRW method
• Stopped perturbed random walks
• Stopped random walks
• Stopping time

Subject Classifications:

• 60F05
• 60F15
• 60G40
• 60G50
• 60K05
• 62L10

ACKNOWLEDGMENT

I wish to thank the Editor, Professor Nitis Mukhopadhyay, for inviting me to write this article and for his encouragement.

Notes

Recommended by N. Mukhopadhyay