Finance Papers

Document Type

Journal Article

Date of this Version

5-2015

Publication Source

The American Mathematical Monthly

Volume

122

Issue

5

Start Page

490

Last Page

494

Abstract

In 1964 A. Garsia gave a stunningly brief proof of a useful maximal inequality of E. Hopf. The proof has become a textbook standard, but the inequality and its proof are widely regarded as mysterious. Here we suggest a straightforward first step analysis that may dispel some of the mystery. The development requires little more than the notion of a random variable, and, the inequality may be introduced as early as one likes in a graduate probability course. The benefit is that one gains access to a proof of the strong law of large numbers that is pleasantly free of technicalities or tricky ideas.

Copyright/Permission Statement

Copyright © 2015 by Mathematical Association of America.

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Date Posted: 27 November 2017

This document has been peer reviewed.