LEADER 03927nam 22006972 450 001 9910818152303321 005 20151005020622.0 010 $a1-107-23077-2 010 $a1-280-87800-2 010 $a1-139-37878-3 010 $a9786613719317 010 $a1-139-37592-X 010 $a1-139-08465-8 010 $a1-139-38021-4 010 $a1-139-37193-2 010 $a1-139-37735-3 035 $a(CKB)2670000000209345 035 $a(EBL)880643 035 $a(OCoLC)797919775 035 $a(SSID)ssj0000678525 035 $a(PQKBManifestationID)11387200 035 $a(PQKBTitleCode)TC0000678525 035 $a(PQKBWorkID)10727618 035 $a(PQKB)10353791 035 $a(UkCbUP)CR9781139084659 035 $a(Au-PeEL)EBL880643 035 $a(CaPaEBR)ebr10574349 035 $a(CaONFJC)MIL371931 035 $a(MiAaPQ)EBC880643 035 $a(PPN)261286447 035 $a(EXLCZ)992670000000209345 100 $a20110506d2012|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNormal approximations with Malliavin calculus $efrom Stein's method to universality /$fIvan Nourdin, Giovanni Peccati$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2012. 215 $a1 online resource (xiv, 239 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v192 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-01777-7 320 $aIncludes bibliographical references and index. 327 $aMalliavin operators in the one-dimensional case -- Malliavin operators and isonormal Gaussian processes -- Stein's method for one-dimensional normal approximations -- Multidimensional Stein's method -- Stein meets Malliavin : univariate normal approximations -- Multivariate normal approximations -- Exploring the Breuer-Major theorem -- Computation of cumulants -- Exact asymptotics and optimal rates -- Density estimates -- Homogeneous sums and universality -- Gaussian elements, cumulants and Edgeworth expansions -- Hilbert space notation -- Distances between probability measures -- Fractional Brownian motion -- Some results from functional analysis. 330 $aStein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer-Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus. 410 0$aCambridge tracts in mathematics ;$v192. 606 $aApproximation theory 606 $aMalliavin calculus 615 0$aApproximation theory. 615 0$aMalliavin calculus. 676 $a519.2/3 686 $aMAT029000$2bisacsh 700 $aNourdin$b Ivan$0480277 702 $aPeccati$b Giovanni$f1975- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910818152303321 996 $aNormal approximations with Malliavin calculus$93937542 997 $aUNINA