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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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(p.229) 15 Martingales
Stochastic Limit Theory

James Davidson

Oxford University Press

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

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