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On Stein's method for infinitely divisible laws with finite first moment

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On Stein's method for infinitely divisible laws with finite first moment/ by Benjamin Arras, Christian Houdre.
Author:	Arras, Benjamin.
other author:	Houdre, Christian.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xi, 104 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Distribution (Probability theory) -
Online resource:	https://doi.org/10.1007/978-3-030-15017-4
ISBN:	9783030150174

On Stein's method for infinitely divisible laws with finite first moment
Arras, Benjamin.

On Stein's method for infinitely divisible laws with finite first moment[electronic resource] /by Benjamin Arras, Christian Houdre. - Cham :Springer International Publishing :2019. - xi, 104 p. :ill., digital ;24 cm. - SpringerBriefs in probability and mathematical statistics,2365-4333. - SpringerBriefs in probability and mathematical statistics..

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.

ISBN: 9783030150174

Standard No.: 10.1007/978-3-030-15017-4doiSubjects--Topical Terms:

527721
Distribution (Probability theory)

LC Class. No.: QA273.6 / .A77 2019

Dewey Class. No.: 519.2

On Stein's method for infinitely divisible laws with finite first moment
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520 $a 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.
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