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Daley D.J. Vere-Jones D. (2002) An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Second Edition.Размер файла: На удаленном сервере Раздел: Математика >>Матанализ Книга была скачана: 3585 раз Краткое содержание/Аннотация:In preparing this second edition, we have taken the opportunity to reshape the book, partly in response to the further explosion of material on point processes that has occurred in the last decade but partly also in the hope of making some of the material in later chapters of the first edition more accessible to readers primarily interested in models and applications. Topics such as conditional intensities and spatial processes, which appeared relatively advanced and technically difficult at the time of the first edition, have now been so extensively used and developed that they warrant inclusion in the earlier introductory part of the text. Although the original aim of the book-to present an introduction to the theory in as broad a manner as we are able-has remained unchanged, it now seems to us best accomplished in two volumes, the first concentrating on introductory material and models and the second on structure and general theory. The major revisions in this volume, as well as the main new material, are to be found in Chapters 6-8. The rest of the book has been revised to take these changes into account, to correct errors in the first edition, and to bring in a range of new ideas and examples.Even at the time of the first edition, we were struggling to do justice to the variety of directions, applications and links with other material that the theory of point processes had acquired. The situation now is a great deal more daunting. The mathematical ideas, particularly the links to statistical mechanics and with regard to inference for point processes, have extended considerably. Simulation and related computational methods have developed even more rapidly, transforming the range and nature of the problems under active investigation and development. Applications to spatial point patterns, especially in connection with image analysis but also in many other scientific disciplines, have also exploded, frequently acquiring special language and techniques in the different fields of application. Marked point processes, which were clamouring for greater attention even at the time of the first edition, have acquired a central position in many of these new applications, influencing both the direction of growth and the centre of gravity of the theory. We are sadly conscious of our inability to do justice to this wealth of new material. Even less than at the time of the first edition can the book claim to provide a comprehensive, up-to-the-minute treatment of the subject. Nor are we able to provide more than a sketch of how the ideas of the subject have evolved. Nevertheless, we hope that the attempt to provide an introduction to the main lines of development, backed by a succinct yet rigorous treatment of the theory, will prove of value to readers in both theoretical and applied fields and a possible starting point for the development of lecture courses on different facets of the subject. As with the first edition, we have endeavoured to make the material as self-contained as possible, with references to background mathematical concepts summarized in the appendices, which appear in this edition at the end of Volume I. We would like to express our gratitude to the readers who drew our attention to some of the major errors and omissions of the first edition and will be glad to receive similar notice of those that remain or have been newly introduced. Space precludes our listing these many helpers, but we would like to acknowledge our indebtedness to Rick Schoenberg, Robin Milne, Volker Schmidt, GЁunter Last, Peter Glynn, Olav Kallenberg, Martin Kalinke, Jim Pitman, Tim Brown and Steve Evans for particular comments and careful reading of the original or revised texts (or both). Finally, it is a pleasure to thank John Kimmel of Springer-Verlag for his patience and encouragement, and especially Eileen Dallwitz for undertaking the painful task of rekeying the text of the first edition. Daley D.J. Vere-Jones D. (2002) An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Second Edition. |
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