On Stein's Method for Infinitely Divisible Laws with Finite First Moment

• Main Authors: Arras, Benjamin (Author, http://id.loc.gov/vocabulary/relators/aut), Houdré, Christian (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: SpringerBriefs in Probability and Mathematical Statistics,
• Subjects: Probabilities.; Probability Theory and Stochastic Processes.

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 ident...

Table of Contents:

• 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.