Lévy Processes ICM Edition (Cambridge Tracts in Mathematics, Series Number 121) - Softcover

Bertoin, Jean

Softcover

ISBN 10: 0521170044 ISBN 13: 9780521170048

Publisher: Cambridge University Press, 2010

Synopsis

This 1996 book is a comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.

About this title

Review

'At last! For many years, the stochastic community has awaited the publication of a textbook on Lévy processes ... Here it is ... The author presents us with a thorough, concise and very readable account ... It also forms the ideal source on which to base a (post) graduate course on the subject ... the book is a gem and belongs on every probabilist's bookshelves.' P. A. L. Embrechts, Short Book Reviews

' ... an up-to-date and comprehensive account of the theory of Lévy processes.' L'Enseignement Mathématique

'I think this is THE book on the subject, rather than A book on it. The text is clearly written, and very well organised. The subject-matter is mainstream probability, so will always be topical. A book on these lines has been long overdue ... I see the book as being both accessible enough for rookies to learn the subject from it, and authoritative enough for specialists to use for reference.' Professor Nick Bingham, Burbeck College

'This book would form an excellent text for a graduate course intended for probabilists. But it also provides a quick way of accessing and understanding fifty years of the work of many researchers. I strongly approve of both the choice of material and the pleasant manner in which it has been assembled.' S. J. Taylor, Bulletin of the London Mathematical Society

' ... this concise book promises to be the standard reference for students and researchers concerned with this field.' International Mathematical News

Book Description

This 1996 book is a comprehensive account of the theory of Lévy processes. Professor Bertoin uses the interplay between the probabilistic structure and analytic tools to give a quick and concise treatment of the core theory, with the minimum of technical requirements.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2010
• Language: English
• ISBN 10: 0521170044
• ISBN 13: 9780521170048
• Binding: Paperback