國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Upper and lower bounds for stochasti...

SpringerLink (Online service)

Upper and lower bounds for stochastic processesdecomposition theorems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Upper and lower bounds for stochastic processesby Michel Talagrand.
其他題名:	decomposition theorems /
作者:	Talagrand, Michel.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xviii, 726 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Stochastic processes.
電子資源:	https://doi.org/10.1007/978-3-030-82595-9
ISBN:	9783030825959$q(electronic bk.)

Upper and lower bounds for stochastic processesdecomposition theorems /
Talagrand, Michel.

Upper and lower bounds for stochastic processesdecomposition theorems /[electronic resource] :by Michel Talagrand. - Second edition. - Cham :Springer International Publishing :2021. - xviii, 726 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics,v. 602197-5655 ;. - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / A series of modern surveys in mathematics ;v.72..

1. What is This Book About? Part I The Generic Chaining -- 2 Gaussian Processes and the Generic Chaining -- 3 Trees and Other Measures of Size -- 4 Matching Theorems -- Part II Some Dreams Come True -- 5 Warming Up with p-Stable Processes -- 6 Bernoulli Processes -- 7 Random Fourier Series and Trigonometric Sums -- 8 Partitioning Scheme and Families of Distances -- 9 Peaky Part of Functions -- 10 Proof of the Bernoulli Conjecture -- 11 Random Series of Functions -- 12 Infinitely Divisible Processes -- 13 Unfulfilled Dreams -- Part III Practicing -- 14 Empirical Processes, II -- 15 Gaussian Chaos -- 16 Convergence of Orthogonal Series; Majorizing Measures -- 17 Shor's Matching Theorem -- 18 The Ultimate Matching Theorem in Dimension Three -- 19 Application to Banach Space Theory -- A Discrepancy for Convex Sets -- B Some Deterministic Arguments -- C Classical View of Infinitely Divisible Processes -- D Reading Suggestions -- E Research Directions -- F Solutions of Selected Exercises -- G Comparison with the First Edition -- References -- Index.

This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist's toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author's influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.

ISBN: 9783030825959$q(electronic bk.)

Standard No.: 10.1007/978-3-030-82595-9doiSubjects--Topical Terms:

181874
Stochastic processes.

LC Class. No.: QA274 / .T35 2021

Dewey Class. No.: 519.23

Upper and lower bounds for stochastic processesdecomposition theorems /
LDR:03478nmm a2200361 a 4500 001 612435
003 DE-He213
005 20211220211213.0
006 m d
007 cr nn 008maaau
008 220526s2021 sz s 0 eng d
020 $a 9783030825959$q(electronic bk.)
020 $a 9783030825942$q(paper)
024 7 $a 10.1007/978-3-030-82595-9 $2 doi
035 $a 978-3-030-82595-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274 $b .T35 2021
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 519.23 $2 23
090 $a QA274 $b .T137 2021
100 1 $a Talagrand, Michel. $3 256456
245 1 0 $a Upper and lower bounds for stochastic processes $h [electronic resource] : $b decomposition theorems / $c by Michel Talagrand.
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xviii, 726 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics, $x 2197-5655 ; $v v. 60
505 0 $a 1. What is This Book About? Part I The Generic Chaining -- 2 Gaussian Processes and the Generic Chaining -- 3 Trees and Other Measures of Size -- 4 Matching Theorems -- Part II Some Dreams Come True -- 5 Warming Up with p-Stable Processes -- 6 Bernoulli Processes -- 7 Random Fourier Series and Trigonometric Sums -- 8 Partitioning Scheme and Families of Distances -- 9 Peaky Part of Functions -- 10 Proof of the Bernoulli Conjecture -- 11 Random Series of Functions -- 12 Infinitely Divisible Processes -- 13 Unfulfilled Dreams -- Part III Practicing -- 14 Empirical Processes, II -- 15 Gaussian Chaos -- 16 Convergence of Orthogonal Series; Majorizing Measures -- 17 Shor's Matching Theorem -- 18 The Ultimate Matching Theorem in Dimension Three -- 19 Application to Banach Space Theory -- A Discrepancy for Convex Sets -- B Some Deterministic Arguments -- C Classical View of Infinitely Divisible Processes -- D Reading Suggestions -- E Research Directions -- F Solutions of Selected Exercises -- G Comparison with the First Edition -- References -- Index.
520 $a This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist's toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author's influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.
650 0 $a Stochastic processes. $3 181874
650 0 $a Gaussian processes. $3 211434
650 1 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Functional Analysis. $3 274845
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / A series of modern surveys in mathematics ; $v v.72. $3 901716
856 4 0 $u https://doi.org/10.1007/978-3-030-82595-9
950 $a Mathematics and Statistics (SpringerNature-11649)