An Introduction to the Theory of Point Processes

Fully revised and updated by the authors who have reworked their 1988 first edition, this brilliant book brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition.

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.

Point processes and random measures are widely applied in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology Volume One incorporates introductory material from the First Edition with a foretaste of more advanced concepts Volume Two builds on general theory with additional material on marked and spatial processes Abundant examples both reinforce core understanding and illustrate further applications of the models

Inhalt
Basic Theory of Random Measures and Point Processes.- Special Classes of Processes.- Convergence Concepts and Limit Theorems.- Stationary Point Processes and Random Measures.- Palm Theory.- Evolutionary Processes and Predictability.- Spatial Point Processes.