Introductory Lectures on Fluctuations of Lévy Processes with Applications

Andreas E. Kyprianou (Autor)

Buch | Softcover

XIII, 378 Seiten

2006 | 2006
Springer Berlin (Verlag)
978-3-540-31342-7 (ISBN)

Infos

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.

Autor

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.

Inhalt

Lévy processes and applications.- The Lévy-Itô decomposition and path structure.- More distributional and path related properties.- Subordinators at first passage and renewal measures.- General storage models and paths of bounded variation.- The Wiener-Hopf factorisation.- Lévy processes at first passage and insurance risk.- Exit problems for spectrally negative processes.- Applications to optimal stopping problems. Continuous state branching processes and other applications.

Produkt-Details

• Erscheint lt. Verlag: 25.7.2006
• Reihe/Serie: Universitext
• Zusatzinfo: XIII, 378 p. 22 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 595 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: applied probability • Branching Process • differential equation • fluctuation theory • Lévy process • Lévy processes • Maximum • potential analysis • Random Walk • random walks • Stochastic process • Stochastic Processes
• ISBN-10: 3-540-31342-7 / 3540313427
• ISBN-13: 978-3-540-31342-7 / 9783540313427
• Zustand: Neuware