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Andreas E. Kyprianou, University of Bath, UK
Introductory Lectures on Fluctuations of
Lévy Processes with Applications
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. This textbook 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.
Contents: 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.
2006 XIII, 378 p. 22 illus. Softcover
Universitext
► € 39.95 | £ 30.50 ► Conference price: € 31.96 | £ 24.40
ISBN: 978-3-540-31342-7
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Kyprianou, Fluctuation of Lévy Processes with Applications (Universitext)
ISBN: 978-3-540-31342-7 ► € 39.95 | £ 30.50 ► Conference price: € 31.96 | £ 24.40