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.
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)