D. J. Daley, David Vere-Jones

An Introduction to the Theory of Point Processes (eBook, PDF)

Volume II: General Theory and Structure

• Format: PDF

Produktbeschreibung

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.

D.J. Daley is recently retired from the Centre for Mathematics and Applications at the Australian National University, with research publications in a diverse range of applied probability models and their analysis; he is coauthor with Joe Gani of an introductory text on epidemic modelling. The Statistical Society of Australia awarded him their Pitman Medal for 2006.

D. Vere-Jones is an Emeritus Professor at Victoria University of Wellington, widely known for his contributions to Markov chains, point processes, applications in seismology, and statistical education. He is a fellow and Gold Medallist of the Royal Society of New Zealand, and a director of the consulting group Statistical Research Associates.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 573
• Erscheinungstermin: 29. Dezember 2007
• Englisch
• ISBN-13: 9780387498355
• Artikelnr.: 37287700

Autorenporträt

D.J. Daley, Australian National University, Canberra, ACT, Australia / D. Vere-Jones, Victoria University, Wellington, New Zealand

Inhaltsangabe

Early History.- Basic Properties of the Poisson Process.- Simple Results for Stationary Point Processes on the Line.- Renewal Processes.- Finite Point Processes.- Models Constructed via Conditioning: Cox, Cluster, and Marked Point Processes.- Conditional Intensities and Likelihoods.- Second-Order Properties of Stationary Point Processes.

Rezensionen

From the reviews of the second edition:

"This is an important treatise on the mathematical theory relevant to a wide variety of random processes...The reader will find excellent treatments of important advanced topics such as Cox, renewal, Wold, marked, cluster, and other specialized processes, plus concise but useful appendices on topology, measure theory, metric spaces, martingales, and the like." Technometrics, May 2004

"This revision splits the lengthy first version into two volumes now subtitled Volume I: Elementary Theory and Methods and Volume II: Models and General Theory and Structure...this first volume is well worth its price." Journal of the American Statistical Association, September 2004

"The theory of point processes has undergone an explosive expansion in the last two decades. There was a genuine need for a single source that would contain a survey of the general theory of Point Process accessible to beginning graduate students and researchers in the field but at the same time would include some of the more recent - though relatively advanced and technically difficult - developments in the area. The present edition of the book addresses that need quite successfully." (Alok Goswami, Sankhya, Vol. 67 (1), 2005)

"It is a pleasure to announce that a second edition of the classic book 'An Introduction to the Theory of Point Processes' has been published. ... many chapters and sections were thoroughly reworked. This holds true in particular for the exercises, which are obviously produced with particular love. ... The reviewer is sure that the owners of the first edition will buy also the second, and for many younger readers it will become the beloved key reference to point processes." (Dietrich Stoyan, Metrika, May, 2004)

"The second edition of this monograph is divided into two volumes. The first one is concentrated on introductory material and models, the second one on structure and general theory. ... suitable as a textbook with many exercises for beginners as well as a source for scientists interested in high level applications of point processes." (Uwe Küchler, Zentralblatt MATH, Vol. 1026, 2004)

"The first edition of this book by two major research workers in the field speedily established itself as an authoritative account of an important and rapidly developing subject. In this substantially revised and expanded second edition, the authors have wisely decided to divide the book into two parts leaving some of the very technical material ... to a second volume. ... The book is likely to establish itself quickly as a major contribution to the field." (D. R. Cox, Short Book Reviews, Vol. 23 (2), 2003)