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Stochastic analysis for poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry

Contributor(s): Material type: TextTextSeries: Bocconi & Springer Series: Mathematics, Statistics, Finance and Economics; 7Publication details: Switzerland Springer 2016Description: xv, 346 pISBN:
  • 9783319052328
Subject(s): DDC classification:
  • 519.22 S8
Summary: 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. http://www.springer.com/gp/book/9783319052328
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-B / Slot 1402 (0 Floor, East Wing) Non-fiction General Stacks 519.22 S8 (Browse shelf(Opens below)) Available 192870

Table of contents:

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.

http://www.springer.com/gp/book/9783319052328

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