LEADER 04325nam 22006615 450 001 9910254065703321 005 20251116160141.0 010 $a3-319-05233-0 024 7 $a10.1007/978-3-319-05233-5 035 $a(CKB)3710000000746188 035 $a(DE-He213)978-3-319-05233-5 035 $a(MiAaPQ)EBC4586203 035 $a(PPN)19451577X 035 $a(EXLCZ)993710000000746188 100 $a20160707d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic analysis for Poisson point processes $eMalliavin calculus, Wiener-Itô chaos expansions and stochastic geometry /$fedited by Giovanni Peccati, Matthias Reitzner 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XV, 346 p. 2 illus. in color.) 225 1 $aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v7 311 08$a3-319-05232-2 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1 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. 330 $aStochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years ? due mainly to the impetus of the authors and their collaborators ? a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets. 410 0$aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v7 606 $aProbabilities 606 $aCombinatorial analysis 606 $aPolytopes 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aPolytopes$3https://scigraph.springernature.com/ontologies/product-market-codes/M21040 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aProbabilities. 615 0$aCombinatorial analysis. 615 0$aPolytopes. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aCombinatorics. 615 24$aPolytopes. 615 24$aApplications of Mathematics. 676 $a519.2 702 $aPeccati$b Giovanni$f1975-$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aReitzner$b Matthias$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254065703321 996 $aStochastic analysis for Poisson point processes$91523651 997 $aUNINA