Overview
- Fills a gap in the market; namely a text which is focused on one of the fundamental corner stones of the theory of Lévy processes and does so in a pedagogical way and at graduate level
- First book within the field which gives a comprehensive set of exercises with fully worked out solutions
- Complementary addition to existing book on Lévy processes - stresses fluctuation theory in the context of classical applied probability models
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is justified by their application in many areas of classical and modern stochastic models.
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. Central to the presentation are decompositions of the paths of Lévy processes in terms of their local maxima and an understanding of their short- and long-term behaviour.
The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness. Each chapter has a comprehensive set of exercises with complete solutions.
Reviews
From the reviews:
"This textbook is an introduction to fine path-properties of real Lévy processes with a view towards applications. … it is written in a more pedagogical tone, with many exercises for which answers are given. … This monograph is mainly intended as a textbook for graduate students, as the author says in the introduction, but it should also be useful for researchers wishing to become better acquainted with the fluctuation theory of Lévy processes, and its applications." (Thomas D. Simon, Mathematical Reviews, Issue 2008 a)
Authors and Affiliations
About the author
Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.
Bibliographic Information
Book Title: Introductory Lectures on Fluctuations of Lévy Processes with Applications
Authors: Andreas E. Kyprianou
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-540-31343-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
eBook ISBN: 978-3-540-31343-4Published: 18 December 2006
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIII, 378
Number of Illustrations: 22 b/w illustrations
Topics: Analysis, Probability Theory and Stochastic Processes, Quantitative Finance