03927nam 22006972 450 991081815230332120151005020622.01-107-23077-21-280-87800-21-139-37878-397866137193171-139-37592-X1-139-08465-81-139-38021-41-139-37193-21-139-37735-3(CKB)2670000000209345(EBL)880643(OCoLC)797919775(SSID)ssj0000678525(PQKBManifestationID)11387200(PQKBTitleCode)TC0000678525(PQKBWorkID)10727618(PQKB)10353791(UkCbUP)CR9781139084659(Au-PeEL)EBL880643(CaPaEBR)ebr10574349(CaONFJC)MIL371931(MiAaPQ)EBC880643(PPN)261286447(EXLCZ)99267000000020934520110506d2012|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierNormal approximations with Malliavin calculus from Stein's method to universality /Ivan Nourdin, Giovanni Peccati[electronic resource]Cambridge :Cambridge University Press,2012.1 online resource (xiv, 239 pages) digital, PDF file(s)Cambridge tracts in mathematics ;192Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-01777-7 Includes bibliographical references and index.Malliavin 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.Stein'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.Cambridge tracts in mathematics ;192.Approximation theoryMalliavin calculusApproximation theory.Malliavin calculus.519.2/3MAT029000bisacshNourdin Ivan480277Peccati Giovanni1975-UkCbUPUkCbUPBOOK9910818152303321Normal approximations with Malliavin calculus3937542UNINA