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Marginal and Functional Quantization of Stochastic Processes

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 extens...

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Detalhes bibliográficos
Main Authors: Luschgy, Harald (Author), Pagès, Gilles (Author)
Autor Corporativo: SpringerLink (Online service)
Formato: Recurso Electrónico livro electrónico
Idioma:inglês
Publicado em: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
Edição:1st ed. 2023.
Colecção:Probability Theory and Stochastic Modelling, 105
Assuntos:
Probabilities.
Telecommunication.
Mathematics > Data processing.
Probability Theory.
Communications Engineering, Networks.
Computational Mathematics and Numerical Analysis.
Acesso em linha:https://doi.org/10.1007/978-3-031-45464-6
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Sumário:
  • 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.

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