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Introductory Lectures on Fluctuations of Lévy Processes with Applications / by Andreas E. Kyprianou
(Universitext. ISSN:21916675)
版 | 1st ed. 2006. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2006 |
本文言語 | 英語 |
大きさ | XIII, 378 p. 22 illus : online resource |
著者標目 | *Kyprianou, Andreas E author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Probabilities LCSH:Social sciences -- Mathematics 全ての件名で検索 FREE:Analysis FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance |
一般注記 | Lévy Processes and Applications -- TheLévy–Itô Decomposition and Path Structure -- More Distributional and Path-Related Properties -- General Storage Models and Paths of Bounded Variation -- Subordinators at First Passage and Renewal Measures -- The Wiener–Hopf Factorisation -- Lévy Processes at First Passage and Insurance Risk -- Exit Problems for Spectrally Negative Processes -- Applications to Optimal Stopping Problems -- Continuous-State Branching Processes 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 mathematical significance is justified by their application in many areas of classical and modern stochastic models including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes. This text book forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. Central to the presentation are decompositions of the paths of Lévy processes in terms of their local maxima and an understanding of their 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 recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness. Each chapter has a comprehensive set of exercises with complete solutions HTTP:URL=https://doi.org/10.1007/978-3-540-31343-4 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540313434 |
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EB00232439 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000117013 |
ISBN | 9783540313434 |
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