Overview
- Over the past 10-15 years, we have seen a revival of general Lévy process theory, as well as a burst of new applications. There is a lively and growing research community in this area
- Expository articles help to disseminate important theoretical and applied research, especially to young researchers like PhD students and postdocs
- The respective chapters will appeal to various target groups
- Presents a unique blend of analysis and stochastics, with many findings appearing for the first time in a monograph
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2099)
Part of the book sub series: Lévy Matters (LEVY)
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Table of contents (8 chapters)
Keywords
About this book
This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes.
This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
Authors and Affiliations
Bibliographic Information
Book Title: Lévy Matters III
Book Subtitle: Lévy-Type Processes: Construction, Approximation and Sample Path Properties
Authors: Björn Böttcher, René Schilling, Jian Wang
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-02684-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-02683-1Published: 28 January 2014
eBook ISBN: 978-3-319-02684-8Published: 16 January 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 199
Number of Illustrations: 1 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Mathematics, general, Functional Analysis, Operator Theory