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

Front Cover
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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Stochastic Analysis for Poisson Processes
1
Combinatorics of Poisson Stochastic Integrals with RandomIntegrands
37
Variational Analysis of Poisson Processes
81
Malliavin Calculus for Stochastic Processes and Random Measures with Independent Increments
102
Introduction to Stochastic Geometry
145
The MalliavinStein Method on the Poisson Space
185
UStatistics in Stochastic Geometry
229
Poisson Point Process Convergence and Extreme Values in Stochastic Geometry
254
UStatistics on the Spherical Poisson Space
295
Determinantal Point Processes
311
Index
343
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information