A Course on Rough Paths: With an Introduction to Regularity Structures
暫譯: 粗路徑課程：附正則結構導論
Friz, Peter K., Hairer, Martin
- 出版商: Springer
- 出版日期: 2020-05-28
- 售價: $2,610
- 貴賓價: 9.5 折 $2,480
- 語言: 英文
- 頁數: 346
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030415554
- ISBN-13: 9783030415556
海外代購書籍(需單獨結帳)
商品描述
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 It -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
商品描述(中文翻譯)
這本書的第二版經過多次更新和新增練習，繼續為讀者提供對粗路徑分析和正則結構的溫和介紹，這些理論為隨機微分方程的分析提供了許多新的見解，最近也應用於隨機偏微分方程。
粗路徑分析提供了構建隨機微分方程的路徑解理論的方法，這在許多方面類似於確定性微分方程的理論，並允許在分析和概率論的論證之間進行清晰的區分。與正則結構理論結合，它形成了一個強大的工具箱，允許在不依賴於特定概率性質（如適應性或鞅性質）的情況下恢復許多經典結果。
這本教科書基本上是自足的，重點放在思想和簡短的論證上，而不是追求最強的陳述。典型的讀者將接觸過高年級本科的分析和概率課程，對於大多數內容來說，只需了解與布朗運動的 It 積分。
來自第一版的評價：
「可以輕鬆用作研究生課程的支持……以易於理解的方式呈現了兩位專家的獨特觀點，他們自己在這一理論上做出了很大貢獻。」- Fabrice Baudouin 在《數學評論》中
「基於這本書開設研究生課程是很容易的……仔細完成所有練習的研究人員將對當前的技術狀態有非常好的印象。」- Nicolas Perkowski 在《Zentralblatt MATH》中
作者簡介
Peter K. Friz is presently Einstein Professor of Mathematics at TU and WIAS Berlin. His previous professional affiliations include Cambridge University and Merrill Lynch, and he holds a PhD from the Courant Institute of New York University. He has made contributions to the understanding of the Navier-Stokes equation as dynamical system, pioneered new asymptotic techniques in financial mathematics and has written many influential papers on the applications of rough path theory to stochastic analysis, ranging from the interplay of rough paths with Malliavin calculus to a (rough-) pathwise view on non-linear SPDEs. Jointly with N. Victoir he authored a monograph on stochastic processes as rough paths.
Martin Hairer KBE FRS is currently Professor of Mathematics at Imperial College London. He has mostly worked in the fields of stochastic partial differential equations in particular, and in stochastic analysis and stochastic dynamics in general. He made fundamental advances in various directions such as the study of hypoelliptic and/or hypocoercive diffusions, the development of an ergodic theory for stochastic PDEs, the systematisation of the construction of Lyapunov functions for stochastic systems, the development of a general theory of ergodicity for non-Markovian systems, multiscale analysis techniques, etc. Most recently, he has worked on applying rough path techniques to the analysis of certain ill-posed stochastic PDEs and introduced the theory of regularity structures. For this work he was awarded the Fields Medal at the 2014 ICM in Seoul.
作者簡介(中文翻譯)
彼得·K·弗里茲（Peter K. Friz）目前是柏林工業大學（TU）和威廉斯數學研究所（WIAS Berlin）的愛因斯坦數學教授。他之前的職
