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

Author(s)

Bibliographic Information

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

Benjamin Arras, Christian Houdré

(SpringerBriefs in probability and mathematical statistics)

Springer, c2019

Available at  / 6 libraries

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Note

Includes bibliographical references (p. 99-102) and index

Description and Table of Contents

Description

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.

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.

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Details

  • NCID
    BB28191289
  • ISBN
    • 9783030150167
  • LCCN
    2019933697
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xi, 104 p.
  • Size
    24 cm
  • Parent Bibliography ID
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