Titlebook: Stochastic Analysis for Poisson Point Processes; Malliavin Calculus, Giovanni Peccati,Matthias Reitzner Book 2016 Springer International P

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Stochastic Analysis for Poisson Point Processes978-3-319-05233-5Series ISSN 2039-1471 Series E-ISSN 2039-148X

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Combinatorics of Poisson Stochastic Integrals with Random Integrands,f functional transforms on the Poisson space. This presentation relies on elementary combinatorics based on the Faà di Bruno formula, partitions and polynomials, which are used together with multiple stochastic integrals, finite difference operators and integration by parts.

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Determinantal Point Processes,n the space of configurations whose invariant measure is the law of a determinantal point process. Second, we present some algorithms to sample from the law of a determinantal point process on a finite window. Related open problems are listed.

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Giovanni Peccati,Matthias ReitznerA self-contained introduction to essential topics in stochastic geometry and infinite-dimensional stochastic analysis.Provides a unique and systematic discussion of Malliavin calculus in the framework

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Book 2016ngs 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 yea

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,-Statistics in Stochastic Geometry,iance estimates, approximation of the covariance structure, and limit theorems which have been out of reach for many years can be derived. In this chapter we state the fundamental properties of .-statistics and investigate moment formulae. The main object of the chapter is to introduce the available limit theorems.

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