An Introduction to the Theory of Point Processes
An Introduction to the Theory of Point Processes
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DOI：
10.1007/978-0-387-49835-5
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发表时间：
2013-08
期刊：
影响因子：
--
通讯作者：
D. Daley;D. Vere-Jones
中科院分区：
文献类型：
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作者：
D. Daley;D. Vere-Jones
点处理和随机测量在电信、地震、图像分析、空间点模式和立体学等领域都有广泛的应用。作者在1988年的第一版中对他们的工作进行了重大的重塑，现在提出了两卷的《点过程理论导论》，配有字幕，第一卷：基本理论和方法，第二卷：一般理论和结构。第一卷包含第一版的介绍性章节，以及基本模型，二阶理论和预测的非正式帐户，目的是使读者主要对模型和应用感兴趣的材料可访问。它还有三个附录，审查主要在第二卷中需要的数学背景。第二卷列出了随机测量和点过程的基本理论在一个统一的设置，并继续与第一版的更多的理论主题：极限定理，遍历理论，棕榈理论，并通过鞅和条件强度的进化行为。非常实质性的新材料在这第二卷包括扩展讨论标记点过程，收敛到平衡，和空间点过程的结构。
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present An Introduction to the Theory of Point Processes in two volumes with subtitles Volume I: Elementary Theory and Methods and Volume II: General Theory and Structure. Volume I contains the introductory chapters from the first edition together with an account of basic models, second order theory, and an informal account of prediction, with the aim of making the material accessible to readers primarily interested in models and applications. It also has three appendices that review the mathematical background needed mainly in Volume II. Volume II sets out the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.