Random measures, theory and applications / Olav Kallenberg
Type de document : MonographieCollection : Probability theory and stochastic modelling, 77Langue : anglais.Pays: Swisse.Éditeur : Cham : Springer , 2017Description : 1vol. (XIII-694 p.) ; 25 cmISBN: 9783319415963.ISSN: 2199-3130.Bibliographie : Bibliogr. p. 657-671. Index.Sujet MSC : 60G55, Probability theory and stochastic processes, Point processes (e.g., Poisson, Cox, Hawkes processes)60G57, Probability theory and stochastic processes, Random measures
60G10, Probability theory and stochastic processes, Stationary stochastic processes
60B05, Probability theory on algebraic and topological structures, Probability measures on topological spaces
60G60, Probability theory and stochastic processes, Random fieldsEn-ligne : zbMath | MSN | Springer
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Monographie
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CMI Salle 1 | 60 KAL (Browse shelf(Opens below)) | Available | 09731-01 |
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. Further, it discusses some areas of application of these concepts, where the abstract theory of random measures contributes decisively to an understanding of the respective application.
Chapters 1 and 2 deal with the fundamental notions and facts concerning random measures and Chapter 3 highlights the basic examples of random measures: Poisson processes, binomial processes, Cox processes, and infinitely divisible random measures. The intermediate Chapters 4–10 develop several different aspects of the general theory: convergence, stationarity, Palm measures, conditioning, compensation, and multiple integrals. Finally, the last three chapters (11–13) deal with select areas of applications of the theory of random measures: stochastic geometry, excursion theory, and branching processes.
The concept of random measures, due to its generality, appears in numerous areas of probability; 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 (MSN)
Bibliogr. p. 657-671. Index
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