Inspired by three continuous-time martingale inequalities that are described in Sect. 12.1, de la Peña et al. (2000, 2004) have developed moment and exponential inequalities for general self-normalized process by making use of the method of mixtures described in Chap. 11. In Sect. 12.2 we present these moment and exponential inequalities under the canonical assumption (10.5) or (10.6) and explain how the method of mixtures can be used to derive them. Their applications are given in Sect. 12.3.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Moment and Exponential Inequalities for Self-Normalized Processes. In: Self-Normalized Processes. Probability and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85636-8_12
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DOI: https://doi.org/10.1007/978-3-540-85636-8_12
Publisher Name: Springer, Berlin, Heidelberg
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