TY - BOOK ID - 46280467 TI - On Stein's Method for Infinitely Divisible Laws with Finite First Moment AU - Arras, Benjamin. AU - Houdré, Christian. PY - 2019 SN - 3030150178 303015016X PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Approximation theory. KW - Theory of approximation KW - Functional analysis KW - Functions KW - Polynomials KW - Chebyshev systems KW - Distribution (Probability theory. KW - Probability Theory and Stochastic Processes. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Probabilities. KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk UR - https://www.unicat.be/uniCat?func=search&query=sysid:46280467 AB - 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. ER -