Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry

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Giovanni Peccati, Matthias Reitzner
Springer, Jul 7, 2016 - Mathematics - 346 pages

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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Stochastic Analysis for Poisson Processes
Combinatorics of Poisson Stochastic Integrals with RandomIntegrands
Variational Analysis of Poisson Processes
Malliavin Calculus for Stochastic Processes and Random Measures with Independent Increments
Introduction to Stochastic Geometry
The MalliavinStein Method on the Poisson Space
UStatistics in Stochastic Geometry
Poisson Point Process Convergence and Extreme Values in Stochastic Geometry
UStatistics on the Spherical Poisson Space
Determinantal Point Processes

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