Bibliograph

Stochastic Analysis for Poisson Point Processes, Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry, edited by Giovanni Peccati, Matthias Reitzner

Type

Label

Stochastic Analysis for Poisson Point Processes, Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry, edited by Giovanni Peccati, Matthias Reitzner

Language

eng

resource.imageBitDepth

Literary Form

non fiction

Main title

Stochastic Analysis for Poisson Point Processes

Medium

electronic resource

Nature of contents

dictionaries

Oclc number

953458901

Responsibility statement

edited by Giovanni Peccati, Matthias Reitzner

Series statement

Springer eBooksBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,, 7, 2039-1471

Sub title

Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry

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.--, Provided by publisher

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

Classification

Contributor