LEADER 04571nam 22006615 450 001 9910726283003321 005 20231115165144.0 010 $a9783031311499$b(electronic bk.) 010 $z9783031311482 024 7 $a10.1007/978-3-031-31149-9 035 $a(MiAaPQ)EBC30545149 035 $a(Au-PeEL)EBL30545149 035 $a(OCoLC)1379855640 035 $a(DE-He213)978-3-031-31149-9 035 $a(BIP)089945406 035 $a(PPN)270615520 035 $a(CKB)26736583000041 035 $a(EXLCZ)9926736583000041 100 $a20230517d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConcentration and Gaussian Approximation for Randomized Sums /$fby Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (438 pages) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v104 311 08$aPrint version: Bobkov, Sergey Concentration and Gaussian Approximation for Randomized Sums Cham : Springer International Publishing AG,c2023 9783031311482 320 $aIncludes bibliographical references and index. 327 $aPart I. Generalities -- 1. Moments and correlation conditions -- 2. Some classes of probability distributions -- 3. Characteristic functions -- 4. Sums of independent random variables -- Part II. Selected topics on concentration -- 5. Standard analytic conditions -- 6. Poincaré-type inequalities -- 7. Logarithmic Sobolev inequalities -- 8. Supremum and infimum convolutions -- Part IV. Analysis on the sphere -- 9. Sobolev-type inequalities -- 10. Second order spherical concentration -- 11. Linear functionals on the sphere -- Part V. First applications to randomized sums -- 12. Typical distributions -- 13. Characteristic functions of weighted sums -- 14. Fluctuations of distributions -- Part VI. Refined bounds and rates -- 15. L^2 expansions and estimates -- 16. Refinements for the Kolmogorov distance -- 17. Applications of the second order correlation condition -- Part VII. Distributions and coefficients of special types -- 18. Special systems and examples -- 19. Distributions with symmetries -- 20. Product measures -- 21. Coefficients of Special type -- Glossary. 330 $aThis book describes extensions of Sudakov's classical result on the concentration of measure phenomenon for weighted sums of dependent random variables. The central topics of the book are weighted sums of random variables and the concentration of their distributions around Gaussian laws. The analysis takes place within the broader context of concentration of measure for functions on high-dimensional spheres. Starting from the usual concentration of Lipschitz functions around their limiting mean, the authors proceed to derive concentration around limiting affine or polynomial functions, aiming towards a theory of higher order concentration based on functional inequalities of log-Sobolev and Poincaré type. These results make it possible to derive concentration of higher order for weighted sums of classes of dependent variables. While the first part of the book discusses the basic notions and results from probability and analysis which are needed for the remainder of the book, the latter parts provide a thorough exposition of concentration, analysis on the sphere, higher order normal approximation and classes of weighted sums of dependent random variables with and without symmetries. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v104 606 $aProbabilities 606 $aMathematical statistics 606 $aProbability Theory 606 $aMathematical Statistics 606 $aDistribució de Gauss$2thub 606 $aDependència (Estadística)$2thub 608 $aLlibres electrònics$2thub 610 $aMathematics 615 0$aProbabilities. 615 0$aMathematical statistics. 615 14$aProbability Theory. 615 24$aMathematical Statistics. 615 7$aDistribució de Gauss 615 7$aDependència (Estadística) 676 $a519.24 700 $aBobkov$b Sergey$01279371 702 $aChistyakov$b Gennadiy 702 $aGo?tze$b Friedrich 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910726283003321 996 $aConcentration and Gaussian Approximation for Randomized Sums$93373759 997 $aUNINA