Random Measures, Theory and Applications

✍ Scribed by Olav Kallenberg

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 702
• Series: Probability Theory and Stochastic Modelling 77
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxviii
Spaces, Kernels, and Disintegration....Pages 15-48
Distributions and Local Structure....Pages 49-69
Poisson and Related Processes....Pages 70-108
Convergence and Approximation....Pages 109-153
Stationarity in Euclidean Spaces....Pages 154-210
Palm and Related Kernels....Pages 211-265
Group Stationarity and Invariance....Pages 266-309
Exterior Conditioning....Pages 310-346
Compensation and Time Change....Pages 347-405
Multiple Integration....Pages 406-446
Line and Flat Processes....Pages 447-480
Regeneration and Local Time....Pages 481-537
Branching Systems and Super-processes....Pages 538-621
Back Matter....Pages 622-694