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Celebrating StatisticsPapers in honour of Sir David Cox on his 80th birthday$
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A. C. Davison, Yadolah Dodge, and N. Wermuth

Print publication date: 2005

Print ISBN-13: 9780198566540

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566540.001.0001

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On some concepts of infinite divisibility and their roles in turbulence, finance and quantum stochastics

On some concepts of infinite divisibility and their roles in turbulence, finance and quantum stochastics

Chapter:
(p.233) 12 On some concepts of infinite divisibility and their roles in turbulence, finance and quantum stochastics
Source:
Celebrating Statistics
Author(s):

Ole Eiler Barndorff-Nielsen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566540.003.0013

This chapter contains an account of contemporary Lévy theory, namely the theory of infinite divisibility, Lévy processes, Lévy bases, and so forth, which has been a very active area of research over the past decade. It surveys a few aspects and ramifications of these developments, the choice of topics being determined by its author’s interests rather than being intended to form a comprehensive overview. After an exposition of classical infinite divisibility and related topics, there is an account of Lévy processes and bases, and of Ornstein-Uhlenbeck processes. A general class of tempospatial models is sketched, and time change, applications to finance and turbulence, and the notion of an upsilon mapping are discussed. The chapter closes with an overview of the links between quantum stochastics and Lévy theory.

Keywords:   chronometer, infinite divisibility, Khintchine formula, Lévy process, Ornstein-Uhlenbeck process, quantum theory, tempospatial model, time change, upsilon mapping

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