Introductory Lectures on Fluctuations of Lévy Processes with Applications
Description
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. 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.
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"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)
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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.