Multidimensional Stochastic Processes as Rough Paths by Peter K. Friz
Multidimensional Stochastic Processes as Rough Paths by Peter K. Friz
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作为粗糙路径的多维随机过程作者：Peter K Friz
DOI：
10.1017/cbo9780511845079
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Nicolas B
中科院分区：
文献类型：
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作者：
Peter K;Victoir;Nicolas B
粗路径分析提供了一个新的视角伊藤的重要理论的随机微分方程。现代随机分析的关键定理（随机流的存在性和极限定理，Freidlin-Wentzell理论，Stroock-Varadhan支持描述）可以通过戏剧性的简化得到。经典的近似结果和它们的局限性（Wong-Zakai，McShane的反例）收到“明显的”粗糙路径的解释。证据是建设粗糙路径将发挥重要作用，在未来的分析随机偏微分方程，作者包括一些第一个结果在这个方向。他们还强调与数学的其他部分，包括Caratheodory几何，狄利克雷形式和Malliavin微积分的相互作用。基于成功的课程在研究生水平，这个最新的介绍提出了粗糙路径理论及其应用随机分析。例子，解释和练习使这本书容易接近研究生和研究人员从各个领域。
Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.