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On Stein's method for infinitely divisible laws with finite first moment
- 作者： Arras, Benjamin, author.
- 其他作者：
- 其他題名：
- SpringerBriefs in probability and mathematical statistics.
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： SpringerBriefs in probability and mathematical statistics,
- 主題： Distribution (Probability theory) , Probability Theory and Stochastic Processes.
- ISBN： 9783030150174 (electronic bk.) 、 9783030150167 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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.
- 摘要註: 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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讀者標籤：
- 系統號： 005452717 | 機讀編目格式
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