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