03151nam 22004575 450 991033826010332120200702200141.03-030-15017-810.1007/978-3-030-15017-4(CKB)4100000007992540(MiAaPQ)EBC5759485(DE-He213)978-3-030-15017-4(PPN)258870591(PPN)235670189(EXLCZ)99410000000799254020190424d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierOn Stein's Method for Infinitely Divisible Laws with Finite First Moment /by Benjamin Arras, Christian Houdré1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (111 pages)SpringerBriefs in Probability and Mathematical Statistics,2365-43333-030-15016-X 1 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.This 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.SpringerBriefs in Probability and Mathematical Statistics,2365-4333ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.511.4Arras Benjaminauthttp://id.loc.gov/vocabulary/relators/aut781676Houdré Christianauthttp://id.loc.gov/vocabulary/relators/autBOOK9910338260103321On Stein's Method for Infinitely Divisible Laws with Finite First Moment2534322UNINA