Fluctuations of Lévy Processes with Applications : Introductory Lectures
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Fluctuations of Lévy Processes with Applications : Introductory Lectures
Resource Information
The work Fluctuations of Lévy Processes with Applications : Introductory Lectures represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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 Fluctuations of Lévy Processes with Applications : Introductory Lectures
 Title remainder
 Introductory Lectures
 Statement of responsibility
 by Andreas E. Kyprianou
 Language
 eng
 Summary
 Lévy processes are the natural continuoustime analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuousstate branching processes and positive selfsimilar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short and longterm 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 tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, WienerHopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive selfsimilar Markov processes. Each chapter has a comprehensive set of exercises. Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and HeriotWatt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability
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 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
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 Universitext,
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