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Random Measures, Theory and Applications
ISBN-13:
9783319415987
Veröffentl:
2017
Seiten:
680
Autor:
Olav Kallenberg
Serie:
77, Probability Theory and Stochastic Modelling
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Preface.- 1.Spaces, Kernels, and Distribution.- 2.Dissection Limits and Regularity.- 3.Poisson and Related Processes.- 4.Convergence and Approximation.- 5.Stationarity in Euclidean Spaces.- 6.Palm and Related Kernels.- 7.Group Stationarity and Invariance.- 8.Exterior Conditioning.- 9.Compensation and Time Change.- 10.Multiple Integration and Chaos.- 11.Line and Flat Processes.- 12.Regeneration and Local Time.- 13.Branching and Superprocesses.- Appendices.- Historical and Bibliographical Notes.- References.- Indices.
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