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.
Universitext
Jacques Istas
Mathematical Modeling for the Life Sciences With 31 Figures
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Jacques Istas D´epartment IMSS BSHM Universit´e Pierre Mend`es-France 38000 Grenoble France e-mail:
[email protected]
Based on the French edition “Introduction aux Mod´elisations Math´ematiques pour les Sciences du Vivant”, Math´ematiques et Applications, Vol. 34, Springer-Verlag 2000
Mathematics Subject Classification (2000): 92B05
Library of Congress Control Number: 2005926252
ISBN-10 3-540-25305-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-25305-1 Springer Berlin Heidelberg New York This work is subject to copyright. All righ