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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.
List of contents
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.
About the author
Olav Kallenberg received his Ph.D. in 1972 from Gothenburg University. After holding various temporary research positions in Sweden and abroad, he emigrated in 1986 to the US, where he became a professor of mathematics at Auburn University. In 1977 he became the second recipient ever of the prestigious Rollo Davidson Prize, in 1989 he was elected a Fellow of the IMS, and in 1991-1994 he served as the editor of
robability Theory and Related Fields. Kallenberg is the author of the previous books "Foundations of Modern Probability", and "Probabilistic Symmetries and Invariance Principles" along with numerous research papers in all areas of probability.
Summary
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.
Additional text
“The theory of random measures is an important point of view of modern probability theory. This is an encyclopedic monograph and the first book to give a systematic treatment of the theory. … the general theory presented in this book is therefore of great importance, far beyond the applications presented here. The book is bound to become the standard reference on the subject.” (Frank Aurzada, Mathematical Reviews, June, 2018)
“This book deals with a different aspects of the theory of random measures. … this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects results which are not easy to find in the literature or even forgotten.” (Nikolai N. Leonenko, zbMATH 1376.60003, 2018)
Report
"The theory of random measures is an important point of view of modern probability theory. This is an encyclopedic monograph and the first book to give a systematic treatment of the theory. ... the general theory presented in this book is therefore of great importance, far beyond the applications presented here. The book is bound to become the standard reference on the subject." (Frank Aurzada, Mathematical Reviews, June, 2018)
"This book deals with a different aspects of the theory of random measures. ... this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects results which are not easy to find in the literature or even forgotten." (Nikolai N. Leonenko, zbMATH 1376.60003, 2018)
