LEADER 03151nam 22004575 450 001 9910338260103321 005 20200702200141.0 010 $a3-030-15017-8 024 7 $a10.1007/978-3-030-15017-4 035 $a(CKB)4100000007992540 035 $a(MiAaPQ)EBC5759485 035 $a(DE-He213)978-3-030-15017-4 035 $z(PPN)258870591 035 $a(PPN)235670189 035 $a(EXLCZ)994100000007992540 100 $a20190424d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOn Stein's Method for Infinitely Divisible Laws with Finite First Moment /$fby Benjamin Arras, Christian Houdré 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (111 pages) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 311 $a3-030-15016-X 327 $a1 Introduction -- 2 Preliminaries -- 3 Characterization and Coupling -- 4 General Upper Bounds by Fourier Methods -- 5 Solution to Stein's Equation for Self-Decomposable Laws -- 6 Applications to Sums of Independent Random Variables. 330 $aThis book focuses on quantitative approximation results for weak limit theorems when the target limiting law is infinitely divisible with finite first moment. Two methods are presented and developed to obtain such quantitative results. At the root of these methods stands a Stein characterizing identity discussed in the third chapter and obtained thanks to a covariance representation of infinitely divisible distributions. The first method is based on characteristic functions and Stein type identities when the involved sequence of random variables is itself infinitely divisible with finite first moment. In particular, based on this technique, quantitative versions of compound Poisson approximation of infinitely divisible distributions are presented. The second method is a general Stein's method approach for univariate selfdecomposable laws with finite first moment. Chapter 6 is concerned with applications and provides general upper bounds to quantify the rate of convergence in classical weak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics. 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a511.4 700 $aArras$b Benjamin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781676 702 $aHoudré$b Christian$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910338260103321 996 $aOn Stein's Method for Infinitely Divisible Laws with Finite First Moment$92534322 997 $aUNINA LEADER 00965nam0-2200301 --450 001 9910986684903321 005 20250402090240.0 010 $a978-88-7466-979-0 020 $aIT$b2024-3105 100 $a20250402d2024----kmuy0itay5050 ba 101 0 $aita$cita 102 $aIT 105 $aa 001yy 200 1 $a<>disturbi del comportamento alimentare$el'approccio della psicoterapia costruttivista intersoggettiva$fClaudia Casini 210 $aRoma$cCarocci$d2024 215 $a166 p.$cill.$d20 cm 225 1 $aTascabili Faber$v285 320 $aContiene bibl. (pp. 157-166) 610 0 $aDisturbi alimentari$aPsicoterapia 676 $a616.85260651$v23$zita 700 1$aCasini,$bClaudia$f<1988- >$01802297 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910986684903321 952 $aCOLLEZ. 1144 (285)$b809/2025$fFSPBC 959 $aFSPBC 996 $aDisturbi del comportamento alimentare$94347924 997 $aUNINA