Random Measures, Theory and Applications

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Springer, Apr 12, 2017 - Mathematics - 680 pages

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.

 

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Contents

Introduction
1
1 Spaces Kernels and Disintegration
15
2 Distributions and Local Structure
49
3 Poisson and Related Processes
70
4 Convergence and Approximation
109
5 Stationarity in Euclidean Spaces
154
6 Palm and Related Kernels
211
7 Group Stationarity and Invariance
266
10 Multiple Integration
406
11 Line and Flat Processes
447
12 Regeneration and Local Time
481
13 Branching Systems and Superprocesses
538
Appendices
622
Historical and Bibliographical Notes
633
References
657
Indices
673

8 Exterior Conditioning
310
9 Compensation and Time Change
347

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About the author (2017)

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.

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