On Stein's method for infinitely divisible laws with finite first moment / Benjamin Arras, Christian Houdré
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 ident...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
[2019]
|
| Series: | Springer briefs in probability and mathematical statistics.
|
| Subjects: |
MARC
| LEADER | 00000cam a2200000xi 4500 | ||
|---|---|---|---|
| 001 | b10469448 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 190504s2019 sz ob 001 0 eng d | ||
| 005 | 20240423172324.8 | ||
| 019 | |a 1099569552 |a 1101400578 |a 1103884217 |a 1105178141 |a 1111066892 |a 1115101291 |a 1117862971 |a 1122812414 |a 1132906611 |a 1156391665 |a 1162719750 | ||
| 020 | |a 9783030150174 |q (electronic book) | ||
| 020 | |a 3030150178 |q (electronic book) | ||
| 020 | |a 9783030150181 |q (print) | ||
| 020 | |a 3030150186 | ||
| 020 | |z 303015016X | ||
| 020 | |z 9783030150167 | ||
| 024 | 7 | |a 10.1007/978-3-030-15017-4 | |
| 024 | 8 | |a 10.1007/978-3-030-15 | |
| 035 | |a (OCoLC)spr1100010841 | ||
| 035 | |a (OCoLC)1100010841 |z (OCoLC)1099569552 |z (OCoLC)1101400578 |z (OCoLC)1103884217 |z (OCoLC)1105178141 |z (OCoLC)1111066892 |z (OCoLC)1115101291 |z (OCoLC)1117862971 |z (OCoLC)1122812414 |z (OCoLC)1132906611 |z (OCoLC)1156391665 |z (OCoLC)1162719750 | ||
| 037 | |a spr978-3-030-15017-4 | ||
| 040 | |a EBLCP |b eng |e rda |e pn |c EBLCP |d YDX |d YDXIT |d UPM |d UKMGB |d OCLCF |d LQU |d OCLCQ |d UKAHL |d VT2 |d LEATE |d OCLCQ |d U@J |d OCLCQ |d SRU |d UAB |d OCLCQ | ||
| 049 | |a GWRE | ||
| 050 | 4 | |a QA273.6 |b .A77 2019 | |
| 100 | 1 | |a Arras, Benjamin, |e author. | |
| 245 | 1 | 0 | |a On Stein's method for infinitely divisible laws with finite first moment / |c Benjamin Arras, Christian Houdré |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2019] | |
| 300 | |a 1 online resource (111 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
| 338 | |a online resource |b cr |2 rdacarrier. | ||
| 347 | |a text file. | ||
| 347 | |b PDF. | ||
| 490 | 1 | |a SpringerBriefs in Probability and Mathematical Statistics, |x 2365-4333. | |
| 504 | |a Includes bibliographical references and index. | ||
| 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. | ||
| 588 | 0 | |a Online resource; title from digital title page (viewed on May 23, 2019) | |
| 650 | 0 | |a Distribution (Probability theory) |0 http://id.loc.gov/authorities/subjects/sh85038545. | |
| 650 | 7 | |a Distribution (Probability theory) |2 fast |0 (OCoLC)fst00895600. | |
| 700 | 1 | |a Houdré, Christian, |e author. |0 http://id.loc.gov/authorities/names/n93122373 |1 http://isni.org/isni/0000000117648442. | |
| 776 | 0 | 8 | |i Print version: |a Arras, Benjamin. |t On Stein's Method for Infinitely Divisible Laws with Finite First Moment. |d Cham : Springer, ©2019 |z 9783030150167. |
| 830 | 0 | |a Springer briefs in probability and mathematical statistics. |0 http://id.loc.gov/authorities/names/no2020149149. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-15017-4 |z Full Text (via Springer) |
| 907 | |a .b104694488 |b 04-01-21 |c 05-15-19 | ||
| 998 | |a web |b 03-31-21 |c b |d b |e - |f eng |g sz |h 0 |i 1 | ||
| 907 | |a .b104694488 |b 03-31-21 |c 05-15-19 | ||
| 944 | |a MARS - RDA ENRICHED | ||
| 915 | |a - | ||
| 956 | |a Springer e-books | ||
| 956 | |b Springer Nature - Springer Mathematics and Statistics eBooks 2019 English International | ||
| 999 | f | f | |i 2c9983d1-80eb-5ddd-b8fa-a006ed43fef3 |s 61f0ef05-2651-5114-9098-381cb60d9922 |
| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e QA273.6 .A77 2019 |h Library of Congress classification |i Ebooks, Prospector |n 1 |