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

Stochastic geometry is the branchof mathematics that studies geometric structures associated with randomconfigurations, such as random graphs, tilings and mosaics. Due to its closeties with stereology and spatial statistics, the results in this area arerelevant for a large number of important applications, e.g. to the mathematicalmodeling and statistical analysis of telecommunication networks, geostatisticsand image analysis. In recent years - due mainly to the impetus of the authorsand their collaborators - a powerful connection has been established betweenstochastic geometry and the Malliavin calculus of variations, which is acollection of probabilistic techniques based on the properties ofinfinite-dimensional differential operators. This has led in particular to thediscovery of a large number of new quantitative limit theorems forhigh-dimensional geometric objects.This unique book presents anorganic collection of authoritative surveys written by the principal act

ors in thisrapidly evolving field, offering a rigorous yet lively presentation of its manyfacets.

1 Stochasticanalysis for Poisson processes.- 2 Combinatorics of Poisson stochasticintegrals with random integrands.- 3 Variational analysis of Poisson processes.-4 Malliavin calculus for stochastic processes and random measures withindependent increments.- 5 Introduction to stochastic geometry.- 6 TheMalliavin-Stein method on the Poisson space.- 7 U-statistics in stochasticgeometry.- 8 Poisson point process convergence and extreme values in stochasticgeometry.- 9 U-statistics on the spherical Poisson space.- 10 Determinantalpoint processes.