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Record Nr. |
UNINA9910254065703321 |
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Titolo |
Stochastic analysis for Poisson point processes : Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry / / edited by Giovanni Peccati, Matthias Reitzner |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
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ISBN |
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Edizione |
[1st ed. 2016.] |
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Descrizione fisica |
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1 online resource (XV, 346 p. 2 illus. in color.) |
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Collana |
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Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics, , 2039-1471 ; ; 7 |
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Disciplina |
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Soggetti |
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Probabilities |
Combinatorial analysis |
Polytopes |
Applied mathematics |
Engineering mathematics |
Probability Theory and Stochastic Processes |
Combinatorics |
Applications of Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and index. |
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Nota di contenuto |
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1 Stochastic analysis for Poisson processes -- 2 Combinatorics of Poisson stochastic integrals with random integrands -- 3 Variational analysis of Poisson processes -- 4 Malliavin calculus for stochastic processes and random measures with independent increments -- 5 Introduction to stochastic geometry -- 6 The Malliavin-Stein method on the Poisson space -- 7 U-statistics in stochastic geometry -- 8 Poisson point process convergence and extreme values in stochastic geometry -- 9 U-statistics on the spherical Poisson space -- 10 Determinantal point processes. |
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Sommario/riassunto |
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Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with |
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stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets. |
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