Brownian motion.Vol. 30.
Brownian motion.Vol. 30.
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布朗运动。卷。
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Y. Peres
中科院分区：
文献类型：
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作者：
Peter Morters;Y. Peres
这本期待已久的教科书涵盖了研究生概率想了解的有关布朗运动的所有内容，以及该领域的最新研究。本书从构建布朗运动开始，然后对路径属性进行采样，例如连续性和无处可微性。分形维数的概念很早就被引入，并在整本书中用于描述布朗路径的精细特性。从多个角度探讨了布朗运动和随机游走的关系，包括从随机游走嵌入发展布朗局部时间理论。引入随机积分作为一种工具，并且对布朗运动势理论的易于处理为广泛处理布朗路径的交点扫清了道路。 Oded Schramm 和 Wendelin Werner 对布朗路径上的特殊点的调查以及对 SLE 过程的附录直接引出了最近的研究主题。
This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.