Introductory Lectures on Fluctuation of Lévy Processes with Applications - Kyprianou, Andreas E.
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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. Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes…mehr

Produktbeschreibung
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. 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 including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes.
This text book 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.
Autorenporträt
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.