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A Course on Rough Paths : With an Introduction to Regularity Structures / by Peter K. Friz, Martin Hairer
(Universitext. ISSN:21916675)
版 | 2nd ed. 2020. |
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出版者 | Cham : Springer International Publishing : Imprint: Springer |
出版年 | 2020 |
大きさ | XVI, 346 p. 3 illus : online resource |
著者標目 | *Friz, Peter K author Hairer, Martin author SpringerLink (Online service) |
件 名 | LCSH:Probabilities LCSH:Differential equations FREE:Probability Theory FREE:Differential Equations |
一般注記 | 1 Introduction -- 2 The space of rough paths -- 3 Brownian motion as a rough path -- 4 Integration against rough paths -- 5 Stochastic integration and Itô’s formula -- 6 Doob–Meyer type decomposition for rough paths -- 7 Operations on controlled rough paths -- 8 Solutions to rough differential equations -- 9 Stochastic differential equations -- 10 Gaussian rough paths -- 11 Cameron–Martin regularity and applications -- 12 Stochastic partial differential equations -- 13 Introduction to regularity structures -- 14 Operations on modelled distributions -- 15 Application to the KPZ equation -- References -- Index With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this … A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH HTTP:URL=https://doi.org/10.1007/978-3-030-41556-3 |
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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 | 9783030415563 |
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電子リソース |
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EB00196877 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000134852 |
ISBN | 9783030415563 |
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※2017年9月4日以降