**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.

**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.

**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.

**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.

**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.

**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.

**Author**: Giuseppe Nicosia

**Publisher:** Springer Nature

**ISBN:** 3030954676

**Category : **
**Languages : **en

**Pages : **
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**Book Description**

**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

**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.

**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.

**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.