Description
Springer Introductory Lectures On Fluctuations Of Levy Processes With Applications 2006 Edition by Andreas E. Kyprianou
This textbook forms the basis of a graduate course on the theory and applications of Levy 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 Levy processes with jumps in only one direction for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness. Table of contents : Levy processes and applications.- The Levy-Ito 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.- Levy 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.