Name: Marginal and Functional Quantization of Stochastic Processes (en Inglés)
Price: 224.39 USD
Availability: InStock
Author: Luschgy, Harald ; Pagès, Gilles
ISBN: 9783031454639

portada Marginal and Functional Quantization of Stochastic Processes (en Inglés)

Marginal and Functional Quantization of Stochastic Processes (en Inglés)

Formato

Libro Físico

Autor

Harald Luschgy

Gilles Pagès

Editorial

Springer

Idioma

Inglés

N° páginas

912

Encuadernación

Tapa Dura

Dimensiones

23.6 x 16.2 x 5.0 cm

Peso

1.70 kg.

ISBN13

9783031454639

Categorías

Fundamentos matemáticos
Probabilidad y estadística
Ingeniería de las comunicaciones/las telecomunicaciones

Marginal and Functional Quantization of Stochastic Processes (en Inglés)

Harald Luschgy (Autor) · Gilles Pagès (Autor) · Springer · Tapa Dura

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Reseña del libro "Marginal and Functional Quantization of Stochastic Processes (en Inglés)"

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.