Random Measures, Theory and Applications. 1st ed. 2017

種類:

電子ブック

責任表示:

by Olav Kallenberg

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Kallenberg, Olav.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 77

ISBN:

9783319415987 [3319415980]    

注記:

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.
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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