國立虎尾科技大學 |

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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	On Stein's method for infinitely divisible laws with finite first moment/ by Benjamin Arras, Christian Houdre.
作者:	Arras, Benjamin.
其他作者:	Houdre, Christian.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xi, 104 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Distribution (Probability theory) -
電子資源:	https://doi.org/10.1007/978-3-030-15017-4
ISBN:	9783030150174

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

On Stein's method for infinitely divisible laws with finite first moment[electronic resource] /by Benjamin Arras, Christian Houdre. - Cham :Springer International Publishing :2019. - xi, 104 p. :ill., digital ;24 cm. - SpringerBriefs in probability and mathematical statistics,2365-4333. - SpringerBriefs in probability and mathematical statistics..

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.

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.

ISBN: 9783030150174

Standard No.: 10.1007/978-3-030-15017-4doiSubjects--Topical Terms:

527721
Distribution (Probability theory)

LC Class. No.: QA273.6 / .A77 2019

Dewey Class. No.: 519.2

On Stein's method for infinitely divisible laws with finite first moment
LDR:02530nam a2200349 a 4500 001 939795
003 DE-He213
005 20190424013711.0
006 m d
007 cr nn 008maaau
008 200414s2019 gw s 0 eng d
020 $a 9783030150174 $q (electronic bk.)
020 $a 9783030150167 $q (paper)
024 7 $a 10.1007/978-3-030-15017-4 $2 doi
035 $a 978-3-030-15017-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA273.6 $b .A77 2019
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
090 $a QA273.6 $b .A773 2019
100 1 $a Arras, Benjamin. $3 1226180
245 1 0 $a On Stein's method for infinitely divisible laws with finite first moment $h [electronic resource] / $c by Benjamin Arras, Christian Houdre.
260 $a Cham : $c 2019. $b Springer International Publishing : $b Imprint: Springer,
300 $a xi, 104 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in probability and mathematical statistics, $x 2365-4333
505 0 $a 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.
520 $a 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.
650 0 $a Distribution (Probability theory) $3 527721
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
700 1 $a Houdre, Christian. $3 1076056
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in probability and mathematical statistics. $3 1070533
856 4 0 $u https://doi.org/10.1007/978-3-030-15017-4
950 $a Mathematics and Statistics (Springer-11649)