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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Marginal and Functional Quantization of Stochastic Processes
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Marginal and Functional Quantization of Stochastic Processes
Harald Luschgy, Gilles Pagès (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
07.12.2023
Sprache
Englisch
EAN
9783031454639
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Probability Theory and Stochastic Modelling
Sonderedition
Nein
Autor
Harald Luschgy, Gilles Pagès
Seitenanzahl
912
Einbandart
Gebundene Ausgabe
Schlagwörter
Vector Quantization, Continuous time stochastic processus, Signal transmission, Cluster algorithms, Space discretizations, Numerical methods in probability, Discretization Methods, Signal processing, Unsupervised learning, Numerical Probability, Pages Numerical Probability, Luschgy Graf, Random Vectors
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
TJK - Nachrichtententechnik, Telekommunikation
PBKS - Numerische Mathematik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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