An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure(Probability and Its Applications)

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 their Introduction to the Theory of Point Processes in two volumes with sub-titles "Elementary Theory and Models" and "General Theory and Structure". Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text. Volume Two returns to the general theory, with additional material on marked and spatial processes. The necessary mathematical background is reviewed in appendices located in Volume One. Daryl Daley is a Senior Fellow in 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 co-author with Joe Gani of an introductory text in epidemic modelling. David Vere-Jones is an Emeritus Professor at Victoria University of Wellington, widely known for his contributions to Markov chains, point processes, applications in seismology.

Table of Contents:
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.

Review :
From the reviews of the second edition: "This book is the second Volume of the original single Volume from 1988, the first volume having appeared in 2003.! It contains several topics that have been studied since 1988, a list of references that is greatly enlarged and improved.! In all, the second volume!serves as an excellent and unique standard reference to the theory of point processes and may not be missed by anyone dealing in a serious way with point processes." (A. Stein, Kwantitatieve Methoden, Issue R12, 2008) "Although the first and second volumes are not physically bound, they are clearly intimately linked.! A welcome new chapter in this second edition provides a brief introduction to spatial point processes surveying both descriptive methods for point patterns and point process models.! Challenging exercises at the end of each chapter both illuminate and expand on the text. The writing flows, yet is always meticulous, all notation is well defined , and a clear love for the subject is transparent throughout. The two volumes together are a major achievement by the authors and deserve to become a main reference in the area of point processes." (Michael Sherman, Journal of the American Statistical Association, March 2009, Vol. 104, No. 485) "The second volume focuses on the structure and general theory of point processes ! . each topic is carefully motivated and an extensive literature review is provided. ! Volume II will be of particular use to the specialist with a good background in probability, measure theory, and topology. ! belong on the shelf of any modern probability theorist." (Gail Ivanoff, Mathematical Reviews, Issue 2009 b)