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 01658nam 22003493a 450 001 9910832945403321 005 20250123132213.0 035 $a(CKB)4970000000226612 035 $a(ScCtBLL)f0db0166-fbcb-4b94-8613-a1917d260e87 035 $a(OCoLC)1000372251 035 $a(EXLCZ)994970000000226612 100 $a20250123i20162016 uu 101 0 $aeng 135 $auru|||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aB.C. Reads: Adult Literacy Fundamental English, Reader Two$fShantel Ivits 210 1$a[s.l.] :$cB.C. Open Textbook Project,$d2016. 215 $a1 online resource (30 p.) 330 $aThis reader, written specifically for adults, contains eight chapters about Langston Hughes' family history and personal life. It includes excerpts from many of Hughes' poems and is designed to accompany the BC Reads: Adult Literacy Fundamental English - Course Pack 2. This level 2 reader, one of a series of six readers, is roughly equivalent to grades 1.5 to 3 in the K-12 system. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This reader has been reviewed by subject experts from colleges and universities. 606 $aLanguage Arts & Disciplines$2bisacsh 606 $aLanguage arts 615 7$aLanguage Arts & Disciplines 615 0$aLanguage arts. 700 $aIvits$b Shantel$01786288 801 0$bScCtBLL 801 1$bScCtBLL 906 $aBOOK 912 $a9910832945403321 996 $aB.C. Reads: Adult Literacy Fundamental English, Reader Two$94318483 997 $aUNINA