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

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

9783030150174 (electronic book)
3030150178 (electronic book)
303015016X
9783030150167

Cham, Switzerland : Springer, [2019]

English

1 online resource (111 pages).

QA273.6 .A77 2019

519.2

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.

Includes bibliographical references and index.

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Description based on online resource; title from digital title page (viewed on May 23, 2019).

SpringerBriefs in Probability and Mathematical Statistics

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