Introductory Lectures on Fluctuations of Lévy Processes with Applications

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.

Andreas Kyprianou is a born and bred Mancunian of Manx-Cypriot descent and recent Mongolian tendencies. He has a degree in Mathematics from Oxford University and a Ph.D. in Probability Theory from Sheffield University. He has held academic positions in Mathematics and Statistics departments at the London School of Economics, Edinburgh University, Utrecht University and, currently, Heriot Watt University, Edinburgh, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.