Harald Luschgy – författare
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10 produkter
10 produkter
Inbunden, Engelska, 2023
2 152 kr
Skickas inom 5-8 vardagar
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.
E-bok
PDF, Engelska, 20232 848 kr
Läs direkt efter köp
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.
Häftad, Engelska, 2024
2 152 kr
Skickas inom 10-15 vardagar
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.
Del 74 - Probability Theory and Stochastic Modelling
Stable Convergence and Stable Limit Theorems
Inbunden, Engelska, 2015
972 kr
Skickas inom 10-15 vardagar
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
E-bok
PDF, Engelska, 20151 258 kr
Läs direkt efter köp
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master''s level with a solid knowledge of measure theoretic probability.
Del 74 - Probability Theory and Stochastic Modelling
Stable Convergence and Stable Limit Theorems
Häftad, Engelska, 2016
972 kr
Skickas inom 10-15 vardagar
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
E-bok
PDF, Engelska, 2007870 kr
Läs direkt efter köp
Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Del 1730 - Lecture Notes in Mathematics
Foundations of Quantization for Probability Distributions
Häftad, Engelska, 2000
650 kr
Skickas inom 10-15 vardagar
Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Häftad, Tyska, 2012
458 kr
Skickas inom 10-15 vardagar
Dieses Lehrbuch bietet neben einer umfassenden Darstellung der Theorie der Martingale in diskreter Zeit auch ausführliche Anwendungen. Die behandelten Themen reichen von klassischem Material über Zerlegungen von stochastischen Prozessen und Submartingalen, quadratische Variation und quadratische Charakteristik, Kompensatoren und Potentiale, Stoppzeiten und gestoppte Prozesse, Ungleichungen, Konvergenz und lokale Konvergenz, starke Gesetze der großen Zahlen, Gesetze vom iterierten Logarithmus und den Zusammenhang mit Markov-Prozessen bis zu neueren Ergebnissen über exponentielle Ungleichungen, einen stabilen zentralen Grenzwertsatz mit exponentieller Rate und die optionale Zerlegung universeller Supermartingale. Die Anwendungen betreffen etwa das finanzmathematische Problem der Optionsbewertung, Verzweigungsprozesse und stochastische Approximationsalgorithmen. Mehr als 170 Übungsaufgaben ergänzen die Darstellung. In der deutschsprachigen Literatur findet man kein vergleichbares Buch..
E-bok
PDF, Tyska, 2012317 kr
Läs direkt efter köp
Dieses Lehrbuch bietet neben einer umfassenden Darstellung der Theorie der Martingale in diskreter Zeit auch ausführliche Anwendungen. Die behandelten Themen reichen von klassischem Material über Zerlegungen von stochastischen Prozessen und Submartingalen, quadratische Variation und quadratische Charakteristik, Kompensatoren und Potentiale, Stoppzeiten und gestoppte Prozesse, Ungleichungen, Konvergenz und lokale Konvergenz, starke Gesetze der großen Zahlen, Gesetze vom iterierten Logarithmus und den Zusammenhang mit Markov-Prozessen bis zu neueren Ergebnissen über exponentielle Ungleichungen, einen stabilen zentralen Grenzwertsatz mit exponentieller Rate und die optionale Zerlegung universeller Supermartingale. Die Anwendungen betreffen etwa das finanzmathematische Problem der Optionsbewertung, Verzweigungsprozesse und stochastische Approximationsalgorithmen. Mehr als 170 Übungsaufgaben ergänzen die Darstellung. In der deutschsprachigen Literatur findet man kein vergleichbares Buch..