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Lévy Processes


Bertoin, J (1998). Lévy Processes. Cambridge: Cambridge University Press.

Abstract

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.

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.

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Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1998
Previous Dates:1996
Deposited On:18 Apr 2013 15:41
Last Modified:05 Apr 2016 16:44
Publisher:Cambridge University Press
Series Name:Cambridge Tracts in Mathematics
Volume:121
Number of Pages:278
ISBN:0-521-56243-0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1406564
http://www.cambridge.org/gb/knowledge/isbn/item1160196

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