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On the Martingales Upcrossings Inequality

Published online by Cambridge University Press:  20 November 2018

M. V. Menon  and
V. Seshadri
M. V. Menon
Affiliation:
University of Missouri, Columbia, Missouri
V. Seshadri
Affiliation:
Mcgill University, Montreal, Quebec
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In this note we present a very simple proof of the upcrossings inequality (see [6], and the note at the end) for martingale sequences—one of the basic results in the theory of martingales—which does not make use of the notion of optional random variable, as is done in the usual proofs of the inequality.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 453 - 454
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Chung, K. L., A course in probability theory, Harcourt Brace, & World Inc., (1968), p. 304.Google Scholar