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Foundations of Quantization for Probability Distributions

Foundations of Quantization for Probability Distributions PDF Author: Siegfried Graf
Publisher: Springer
ISBN: 3540455779
Category : Mathematics
Languages : en
Pages : 230

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Book Description
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.

Foundations of Quantization for Probability Distributions

Foundations of Quantization for Probability Distributions PDF Author: Siegfried Graf
Publisher: Springer
ISBN: 3540455779
Category : Mathematics
Languages : en
Pages : 230

View

Book Description
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.

Foundations of Computational Mathematics, Budapest 2011

Foundations of Computational Mathematics, Budapest 2011 PDF Author: Felipe Cucker
Publisher: Cambridge University Press
ISBN: 1107604079
Category : Computers
Languages : en
Pages : 238

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Book Description
A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.

Numerical Probability

Numerical Probability PDF Author: Gilles Pagès
Publisher: Springer
ISBN: 3319902768
Category : Mathematics
Languages : en
Pages : 579

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Book Description
This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance. Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.

Mathematical Foundation of Turbulent Viscous Flows

Mathematical Foundation of Turbulent Viscous Flows PDF Author: Peter Constantin
Publisher: Springer
ISBN: 3540324542
Category : Mathematics
Languages : en
Pages : 264

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Book Description
Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

Fractal Geometry and Stochastics V

Fractal Geometry and Stochastics V PDF Author: Christoph Bandt
Publisher: Birkhäuser
ISBN: 3319186604
Category : Mathematics
Languages : en
Pages : 340

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Book Description
This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.

Machine Learning, Optimization, and Data Science

Machine Learning, Optimization, and Data Science PDF Author: Giuseppe Nicosia
Publisher: Springer Nature
ISBN: 3030954676
Category :
Languages : en
Pages :

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Mathematical Modelling and Numerical Methods in Finance

Mathematical Modelling and Numerical Methods in Finance PDF Author:
Publisher: Elsevier
ISBN: 0080931006
Category : Mathematics
Languages : en
Pages : 684

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Book Description
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

Construction of Global Lyapunov Functions Using Radial Basis Functions

Construction of Global Lyapunov Functions Using Radial Basis Functions PDF Author: Peter Giesl
Publisher: Springer
ISBN: 3540699090
Category : Mathematics
Languages : en
Pages : 171

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Book Description
The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.

Noncommutative Gröbner Bases and Filtered-Graded Transfer

Noncommutative Gröbner Bases and Filtered-Graded Transfer PDF Author: Huishi Li
Publisher: Springer
ISBN: 3540457658
Category : Mathematics
Languages : en
Pages : 202

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Book Description
This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

Monte Carlo and Quasi-Monte Carlo Methods 2006

Monte Carlo and Quasi-Monte Carlo Methods 2006 PDF Author: Alexander Keller
Publisher: Springer Science & Business Media
ISBN: 3540744967
Category : Mathematics
Languages : en
Pages : 698

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Book Description
This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.