Fluctuations of Lévy Processes with Applications : Introductory Lectures. 2nd ed. 2014

種類:

電子ブック

責任表示:

by Andreas E. Kyprianou

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014

著者名:

• Kyprianou, Andreas E.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783642376320 [3642376320]    

注記:

Lévy processes are the natural continuous-time 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, continuous-state branching processes and positive self-similar 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 long-term 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 rece

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