On Stein’s Method for Infinitely Divisible Laws with Finite First Moment (SpringerBriefs in Probability and Mathematical Statistics) - Softcover

Arras, Benjamin; Houdré, Christian

 
9783030150167: On Stein’s Method for Infinitely Divisible Laws with Finite First Moment (SpringerBriefs in Probability and Mathematical Statistics)
Softcover
ISBN 10: 303015016X ISBN 13: 9783030150167
Verlag: Springer, 2019

Inhaltsangabe

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 classicalweak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.

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Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
303015016X
ISBN 13 
9783030150167
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
116
Kontakt zum Hersteller
Nicht verfügbar
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