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


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This chapter summarizes the essentials of sequential conditioning and martingale theory. After a review of the basic properties of martingales and semi‐martingales, the upcrossing inequality and martingale convergence are studied, and the role of the conditional variances in establishing convergence. The important martingale inequalities of Kolmogorov, Doob, Burkholder, and Azuma are proved.

Keywords: Azuma's inequality; Burkholder's inequality; Doob's inequality; Kolmogorov's inequality; martingale; maximal inequalities; quadratic variation; sequential conditioning; upcrossing inequality

Chapter.  10676 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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