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2014 | OriginalPaper | Buchkapitel

2. The Lévy–Itô Decomposition and Path Structure

verfasst von : Andreas E. Kyprianou

Erschienen in: Fluctuations of Lévy Processes with Applications

Verlag: Springer Berlin Heidelberg

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Abstract

The main aim of this chapter is to establish a rigorous understanding of the structure of the paths of Lévy processes. This will be done by establishing the so-called Lévy–Itô decomposition, which describes the structure of a general Lévy process in terms of three independent auxiliary Lévy processes, each with a different type of path behaviour. In doing so it will be necessary to digress temporarily into the theory of Poisson random measures and associated square-integrable martingales. Understanding the Lévy–Itô decomposition will allow us to distinguish a number of important, but nonetheless general, subclasses of Lévy processes according to their path type. The chapter is concluded with a discussion of the interpretation of the Lévy–Itô decomposition in the context of some of the applied probability models mentioned in Chap. 1.

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Vorheriges Kapitel Lévy Processes and Applications

Nächstes Kapitel More Distributional and Path-Related Properties

Nur mit Berechtigung zugänglich

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Titel: The Lévy–Itô Decomposition and Path Structure
verfasst von: Andreas E. Kyprianou
Verlag: Springer Berlin Heidelberg
Buch: Fluctuations of Lévy Processes with Applications
Print ISBN: 978-3-642-37631-3

Electronic ISBN: 978-3-642-37632-0

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-642-37632-0_2