Olav Kallenberg

Random Measures, Theory and Applications

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Probability Theory and Stochastic Modelling 77
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-41596-3
• 1st ed. 2017
• Seitenzahl: 708
• Erscheinungstermin: 25. April 2017
• Englisch
• Abmessung: 241mm x 160mm x 44mm
• Gewicht: 1206g
• ISBN-13: 9783319415963
• ISBN-10: 3319415964
• Artikelnr.: 45125809

Autorenporträt

Olav Kallenberg (Ph.D., Chalmers University, Gothenburg, Sweden, 1972) is an Emeritus Professor at Auburn University. He has held research positions in Sweden and abroad and taught in the US for more than 30 years. In 1977 he was awarded the Rollo Davidson Prize by Cambridge University, in 1989 he was elected a Fellow of the IMS, and in 1991-94 he served as the editor of PTRF. He has given plenary talks at major conferences all over the world, and was the opening lecturer at both the Vilnius Conference in 2006 and at the SPA Conference in Gothenburg in 2018. Apart from his numerous research papers, he is known for his Springer books Probabilistic Symmetries and Invariance Principles (2005) and Random Measures, Theory and Applications (2017). His book Foundations of Modern Probability (1997, 2002, and 2021) has become a classic reference work.

Inhaltsangabe

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.

Rezensionen

"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)