Abstract
In this chapter we first review basic martingale theory and then introduce tangent sequences and decoupling inequalities which are used to derive exponential inequalities for martingales. These exponential inequalities will be used in Chap. 10 to show that a wide range of stochastic models satisfy certain “canonical assumptions,” under which self-normalized processes can be treated by a general “pseudo-maximization” approach described in Chap. 11.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Martingale Inequalities and Related Tools. In: Self-Normalized Processes. Probability and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85636-8_9
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DOI: https://doi.org/10.1007/978-3-540-85636-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85635-1
Online ISBN: 978-3-540-85636-8
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