Symmetric Markov Processes, Time Change, and Boundary Theory
Symmetric Markov Processes, Time Change, and Boundary Theory
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DOI：
10.1515/9781400840564
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发表时间：
2011-01
期刊：
影响因子：
--
通讯作者：
Zhen-Qing Chen;福島 正俊
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文献类型：
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作者：
Zhen-Qing Chen;福島 正俊
这本书给出了一个全面的和自足的介绍对称马尔可夫过程和对称准经常狄利克雷形式的理论。在一个详细的和可访问的方式，陈振清和Masatoshi福岛涵盖了对称马尔可夫过程理论的基本要素和应用，包括复发/瞬态准则，概率势理论，添加剂功能理论，和时间变化理论。作者在对称拟正则狄利克雷形式的一般框架中以与正则狄利克雷形式统一的方式发展理论，强调扩展狄利克雷空间的作用以及理论的概率和分析方面之间的丰富相互作用。陈和福岛然后地址的最新进展，在这里提出的第一次在任何书籍。主题包括时变马尔可夫过程的表征方面的道格拉斯积分和反射狄利克雷空间的系统性帐户，和重要的角色，这种进步在对称马尔可夫过程的边界理论。这卷是研究人员和从业人员的理想资源，也可以作为高级研究生的教科书。它包括例子、附录和带解答的练习。
This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.