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

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book On Stein's Method for Infinitely Divisible Laws with Finite First Moment by Benjamin Arras, Christian Houdré, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Benjamin Arras, Christian Houdré ISBN: 9783030150174
Publisher: Springer International Publishing Publication: April 24, 2019
Imprint: Springer Language: English
Author: Benjamin Arras, Christian Houdré
ISBN: 9783030150174
Publisher: Springer International Publishing
Publication: April 24, 2019
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Applying Comparative Effectiveness Data to Medical Decision Making by Benjamin Arras, Christian Houdré
Cover of the book Integrated Reporting by Benjamin Arras, Christian Houdré
Cover of the book Fracture Mechanics of Piezoelectric Solids with Interface Cracks by Benjamin Arras, Christian Houdré
Cover of the book New Era for Robust Speech Recognition by Benjamin Arras, Christian Houdré
Cover of the book Health Disparities in Respiratory Medicine by Benjamin Arras, Christian Houdré
Cover of the book Stein Manifolds and Holomorphic Mappings by Benjamin Arras, Christian Houdré
Cover of the book Advances in Knowledge Discovery and Management by Benjamin Arras, Christian Houdré
Cover of the book Realism and Fear in International Relations by Benjamin Arras, Christian Houdré
Cover of the book Rheological and Seismic Properties of Solid-Melt Systems by Benjamin Arras, Christian Houdré
Cover of the book Low-Angle Polarized Neutron and X-Ray Scattering from Magnetic Nanolayers and Nanostructures by Benjamin Arras, Christian Houdré
Cover of the book Interoperability and Open-Source Solutions for the Internet of Things by Benjamin Arras, Christian Houdré
Cover of the book Elise Boulding: Writings on Peace Research, Peacemaking, and the Future by Benjamin Arras, Christian Houdré
Cover of the book Transdisciplinarity for Small-Scale Fisheries Governance by Benjamin Arras, Christian Houdré
Cover of the book Digital Transformation and Global Society by Benjamin Arras, Christian Houdré
Cover of the book Conquest of Body by Benjamin Arras, Christian Houdré
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy