Fluctuations of Lévy Processes with Applications

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.

• Lévy Processes and Applications.- The Lévy–Itô Decomposition and Path Structure.- More Distributional and Path-Related Properties.- General Storage Models and Paths of Bounded Variation.- Subordinators at First Passage and Renewal Measures.- The Wiener–Hopf Factorisation.- Lévy Processes at First Passage.- Exit Problems for Spectrally Negative Processes.- More on Scale Functions.- Ruin Problems and Gerber-Shiu Theory.- Applications to Optimal Stopping Problems.- Continuous-State Branching Processes.- Positive Self-similar Markov Processes.- Epilogue.- Hints for Exercises.- References.- Index.

"The book grew out of lectures pitched at an advanced undergraduate or beginning graduate audience, the prerequisite being a course on abstract Lebesgue integration and a good foundation in probability theory ... . Fluctuations of Levy processes is an interesting book and it is currently the best introduction for the novice to this important topic." (Rene L. Schilling, Mathematical Reviews, April, 2015)