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Stochastic analysis for Poisson poin...

Peccati, Giovanni.

Stochastic analysis for Poisson point processesMalliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic analysis for Poisson point processesedited by Giovanni Peccati, Matthias Reitzner.
其他題名:	Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /
其他作者:	Peccati, Giovanni.
出版者:	Cham :Springer International Publishing :2016.
面頁冊數:	xv, 346 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Poisson processes.
電子資源:	http://dx.doi.org/10.1007/978-3-319-05233-5
ISBN:	9783319052335$q(electronic bk.)

Stochastic analysis for Poisson point processesMalliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /
Stochastic analysis for Poisson point processesMalliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /[electronic resource] :edited by Giovanni Peccati, Matthias Reitzner. - Cham :Springer International Publishing :2016. - xv, 346 p. :ill., digital ;24 cm. - Bocconi & Springer series,v.72039-1471 ;. - Bocconi & Springer series ;v.6..

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.

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 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.

ISBN: 9783319052335$q(electronic bk.)

Standard No.: 10.1007/978-3-319-05233-5doiSubjects--Topical Terms:

191620
Poisson processes.

LC Class. No.: QA274.2 / .S76 2016

Dewey Class. No.: 519.22

Stochastic analysis for Poisson point processesMalliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /
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505 0 $a 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.
520 $a 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 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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