國立高雄大學圖資館 |

Language: English

Back

Marginal and functional quantization of stochastic processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Marginal and functional quantization of stochastic processesby Harald Luschgy, Gilles Pages.
Author:	Luschgy, Harald.
other author:	Pages, Gilles.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xviii, 912 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes.
Online resource:	https://doi.org/10.1007/978-3-031-45464-6
ISBN:	9783031454646$q(electronic bk.)

Marginal and functional quantization of stochastic processes
Luschgy, Harald.

Marginal and functional quantization of stochastic processes[electronic resource] /by Harald Luschgy, Gilles Pages. - Cham :Springer Nature Switzerland :2023. - xviii, 912 p. :ill. (some col.), digital ;24 cm. - Probability theory and stochastic modelling,v. 1052199-3149 ;. - Probability theory and stochastic modelling ;v.70..

Preface -- Notation Index -- Part I. Basics and Marginal Quantization -- 1. Optimal and Stationary Quantizers -- 2. The Finite-Dimensional Setting I -- 3. The Finite-Dimensional Setting II -- Part II. Functional Quantization -- 4. Functional Quantization, Small Ball Probabilities, Metric Entropy and Series Expansions for Gaussian Processes -- 5. Spectral Methods for Gaussian Processes -- 6. Geometry of Optimal and Rate-Optimal Quantizers for Gaussian Processes -- 7. Mean Regular Processes -- Part III. Algorithmic Aspects and Applications:- 8. Optimal Quantization from the Numerical Side (Static) -- 9. Applications: Quantization-Based Cubature Formulas -- 10. Quantization-Based Numerical Schemes -- Appendices -- A. Radon Random Vectors, Stochastic Processes and Inequalities -- B. Miscellany -- References -- Index.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space-a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

ISBN: 9783031454646$q(electronic bk.)

Standard No.: 10.1007/978-3-031-45464-6doiSubjects--Topical Terms:

181874
Stochastic processes.

LC Class. No.: QA274

Dewey Class. No.: 519.23

Marginal and functional quantization of stochastic processes
LDR:03899nmm a2200361 a 4500 001 653421
003 DE-He213
005 20231206172107.0
006 m d
007 cr nn 008maaau
008 240426s2023 sz s 0 eng d
020 $a 9783031454646$q(electronic bk.)
020 $a 9783031454639$q(paper)
024 7 $a 10.1007/978-3-031-45464-6 $2 doi
035 $a 978-3-031-45464-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274
072 7 $a PBT $2 bicssc
072 7 $a PBWL $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 .L968 2023
100 1 $a Luschgy, Harald. $3 468023
245 1 0 $a Marginal and functional quantization of stochastic processes $h [electronic resource] / $c by Harald Luschgy, Gilles Pages.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xviii, 912 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Probability theory and stochastic modelling, $x 2199-3149 ; $v v. 105
505 0 $a Preface -- Notation Index -- Part I. Basics and Marginal Quantization -- 1. Optimal and Stationary Quantizers -- 2. The Finite-Dimensional Setting I -- 3. The Finite-Dimensional Setting II -- Part II. Functional Quantization -- 4. Functional Quantization, Small Ball Probabilities, Metric Entropy and Series Expansions for Gaussian Processes -- 5. Spectral Methods for Gaussian Processes -- 6. Geometry of Optimal and Rate-Optimal Quantizers for Gaussian Processes -- 7. Mean Regular Processes -- Part III. Algorithmic Aspects and Applications:- 8. Optimal Quantization from the Numerical Side (Static) -- 9. Applications: Quantization-Based Cubature Formulas -- 10. Quantization-Based Numerical Schemes -- Appendices -- A. Radon Random Vectors, Stochastic Processes and Inequalities -- B. Miscellany -- References -- Index.
520 $a Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space-a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.
650 0 $a Stochastic processes. $3 181874
650 1 4 $a Probability Theory. $3 913371
650 2 4 $a Communications Engineering, Networks. $3 273745
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 274020
700 1 $a Pages, Gilles. $3 681163
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Probability theory and stochastic modelling ; $v v.70. $3 683306
856 4 0 $u https://doi.org/10.1007/978-3-031-45464-6
950 $a Mathematics and Statistics (SpringerNature-11649)