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SpringerBriefs in Probability and Mathematical Statistics

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

Authors: Arras, Benjamin, Houdré, Christian

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  • Covers connections between infinite divisibility and Stein's method
  • First to propose a general and unifying Stein's methodology for infinitely divisible law with finite first moment
  • Provides quantitative versions of classical weak limit theories for sum of independent random variables
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  • ISBN 978-3-030-15017-4
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About this book

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.

Reviews

“The book is interesting and well written. It may be recommended as a must-have item to the researchers interested in limit theorems of probability theory as well as to other probability theorists.” (Przemysław matuła, Mathematical Reviews, January, 2020)

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-030-15017-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
On Stein's Method for Infinitely Divisible Laws with Finite First Moment
Authors
Series Title
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-15017-4
DOI
10.1007/978-3-030-15017-4
Softcover ISBN
978-3-030-15016-7
Series ISSN
2365-4333
Edition Number
1
Number of Pages
XI, 104
Number of Illustrations
1 b/w illustrations
Topics