An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure

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Springer Science & Business Media, Nov 12, 2007 - Mathematics - 573 pages

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.

 

Contents

Chapter Titles for Volume I
1
Basic Theory of Random Measures and Point Processes
9
Convergence Concepts and Limit Theorems
131
Stationary Point Processes and Random Measures
176
Palm Theory
268
Evolutionary Processes and Predictability
355
A1 A Review of Some Basic Concepts
368
A2 Measures on Metric Spaces
384
A3 Conditional Expectations Stopping Times and Martingales
414
Spatial Point Processes
457
References with Index
537
Subject Index
557
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