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Theory Of Stochastic Canonical Equations
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Author :Vi︠a︡cheslav Leonidovich Girko Publisher :Springer Science & Business Media ISBN 13 :9781402000744 Total Pages :496 pages Book Rating :4.0/5 (7 download)
Book Synopsis Theory of Stochastic Canonical Equations by : Vi︠a︡cheslav Leonidovich Girko
Download or read book Theory of Stochastic Canonical Equations written by Vi︠a︡cheslav Leonidovich Girko and published by Springer Science & Business Media. This book was released on 2001 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Stochastic Canonical Equations by : V.L. Girko
Download or read book Theory of Stochastic Canonical Equations written by V.L. Girko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Stochastic Canonical Equations collects the major results of thirty years of the author's work in the creation of the theory of stochastic canonical equations. It is the first book to completely explore this theory and to provide the necessary tools for dealing with these equations. Included are limit phenomena of sequences of random matrices and the asymptotic properties of the eigenvalues of such matrices. The book is especially interesting since it gives readers a chance to study proofs written by the mathematician who discovered them. All fifty-nine canonical equations are derived and explored along with their applications in such diverse fields as probability and statistics, economics and finance, statistical physics, quantum mechanics, control theory, cryptography, and communications networks. Some of these equations were first published in Russian in 1988 in the book Spectral Theory of Random Matrices, published by Nauka Science, Moscow. An understanding of the structure of random eigenvalues and eigenvectors is central to random matrices and their applications. Random matrix analysis uses a broad spectrum of other parts of mathematics, linear algebra, geometry, analysis, statistical physics, combinatories, and so forth. In return, random matrix theory is one of the chief tools of modern statistics, to the extent that at times the interface between matrix analysis and statistics is notably blurred. Volume I of Theory of Stochastic Canonical Equations discusses the key canonical equations in advanced random matrix analysis. Volume II turns its attention to a broad discussion of some concrete examples of matrices. It contains in-depth discussion of modern, highly-specialized topics in matrix analysis, such as unitary random matrices and Jacoby random matrices. The book is intended for a variety of readers: students, engineers, statisticians, economists and others.
Book Synopsis Quadratic Vector Equations on Complex Upper Half-Plane by : Oskari Ajanki
Download or read book Quadratic Vector Equations on Complex Upper Half-Plane written by Oskari Ajanki and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the nonlinear equation −1m=z+Sm with a parameter z in the complex upper half plane H, where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. In this paper the authors give a comprehensive analysis of these singularities with uniform quantitative controls. They also find a universal shape describing the transition regime between the square root and cubic root singularities. Finally, motivated by random matrix applications in the authors' companion paper they present a complete stability analysis of the equation for any z∈H, including the vicinity of the singularities.
Book Synopsis Random Matrices and Non-Commutative Probability by : Arup Bose
Download or read book Random Matrices and Non-Commutative Probability written by Arup Bose and published by CRC Press. This book was released on 2021-10-26 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Book Synopsis Advances in Multiuser Detection by : Michael L. Honig
Download or read book Advances in Multiuser Detection written by Michael L. Honig and published by John Wiley & Sons. This book was released on 2009-08-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Timely Exploration of Multiuser Detection in Wireless Networks During the past decade, the design and development of current and emerging wireless systems have motivated many important advances in multiuser detection. This book fills an important need by providing a comprehensive overview of crucial recent developments that have occurred in this active research area. Each chapter is contributed by noted experts and is meant to serve as a self-contained treatment of the topic. Coverage includes: Linear and decision feedback methods Iterative multiuser detection and decoding Multiuser detection in the presence of channel impairments Performance analysis with random signatures and channels Joint detection methods for MIMO channels Interference avoidance methods at the transmitter Transmitter precoding methods for the MIMO downlink This book is an ideal entry point for exploring ongoing research in multiuser detection and for learning about the field's existing unsolved problems and issues. It is a valuable resource for researchers, engineers, and graduate students who are involved in the area of digital communications.
Book Synopsis Brownian Motion and Stochastic Calculus by : Ioannis Karatzas
Download or read book Brownian Motion and Stochastic Calculus written by Ioannis Karatzas and published by Springer. This book was released on 2014-03-27 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
Author :Kandethody M. Ramachandran Publisher :Springer Science & Business Media ISBN 13 :9491216473 Total Pages :253 pages Book Rating :4.4/5 (912 download)
Book Synopsis Stochastic Differential Games. Theory and Applications by : Kandethody M. Ramachandran
Download or read book Stochastic Differential Games. Theory and Applications written by Kandethody M. Ramachandran and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
Book Synopsis Singular Perturbation Theory by : R.S. Johnson
Download or read book Singular Perturbation Theory written by R.S. Johnson and published by Springer Science & Business Media. This book was released on 2005-12-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.
Book Synopsis An Introduction to Statistical Analysis of Random Arrays by : Vâčeslav Leonidovič Girko
Download or read book An Introduction to Statistical Analysis of Random Arrays written by Vâčeslav Leonidovič Girko and published by VSP. This book was released on 1998 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the results of 30 years of investigation by the author into the creation of a new theory on statistical analysis of observations, based on the principle of random arrays of random vectors and matrices of increasing dimensions. It describes limit phenomena of sequences of random observations, which occupy a central place in the theory of random matrices. This is the first book to explore statistical analysis of random arrays and provides the necessary tools for such analysis. This book is a natural generalization of multidimensional statistical analysis and aims to provide its readers with new, improved estimators of this analysis. The book consists of 14 chapters and opens with the theory of sample random matrices of fixed dimension, which allows to envelop not only the problems of multidimensional statistical analysis, but also some important problems of mechanics, physics and economics. The second chapter deals with all 50 known canonical equations of the new statistical analysis, which form the basis for finding new and improved statistical estimators. Chapters 3-5 contain detailed proof of the three main laws on the theory of sample random matrices. In chapters 6-10 detailed, strong proofs of the Circular and Elliptic Laws and their generalization are given. In chapters 11-13 the convergence rates of spectral functions are given for the practical application of new estimators and important questions on random matrix physics are considered. The final chapter contains 54 new statistical estimators, which generalize the main estimators of statistical analysis.
Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős
Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003-05 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiparametric Statistics by : Vadim Ivanovich Serdobolskii
Download or read book Multiparametric Statistics written by Vadim Ivanovich Serdobolskii and published by Elsevier. This book was released on 2007-10-18 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science.- Presents original mathematical investigations and open a new branch of mathematical statistics- Illustrates a technique for developing always stable and efficient versions of multivariate statistical analysis for large-dimensional problems - Describes the most popular methods some near exact solutions; including algorithms of non-degenerating large-dimensional discriminant and regression analysis
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis The Fokker-planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions by : Christian Soize
Download or read book The Fokker-planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and published by World Scientific. This book was released on 1994-05-16 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
Book Synopsis Robust Adaptive Beamforming by : Jian Li
Download or read book Robust Adaptive Beamforming written by Jian Li and published by Wiley-Interscience. This book was released on 2006 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest research and developments in robust adaptive beamforming Recent work has made great strides toward devising robust adaptive beamformers that vastly improve signal strength against background noise and directional interference. This dynamic technology has diverse applications, including radar, sonar, acoustics, astronomy, seismology, communications, and medical imaging. There are also exciting emerging applications such as smart antennas for wireless communications, handheld ultrasound imaging systems, and directional hearing aids. Robust Adaptive Beamforming compiles the theories and work of leading researchers investigating various approaches in one comprehensive volume. Unlike previous efforts, these pioneering studies are based on theories that use an uncertainty set of the array steering vector. The researchers define their theories, explain their methodologies, and present their conclusions. Methods presented include: Coupling the standard Capon beamformers with a spherical or ellipsoidal uncertainty set of the array steering vector Diagonal loading for finite sample size beamforming Mean-squared error beamforming for signal estimation Constant modulus beamforming Robust wideband beamforming using a steered adaptive beamformer to adapt the weight vector within a generalized sidelobe canceller formulation Robust Adaptive Beamforming provides a truly up-to-date resource and reference for engineers, researchers, and graduate students in this promising, rapidly expanding field.
Book Synopsis Singular General Relativity by : Ovidiu Cristinel Stoica
Download or read book Singular General Relativity written by Ovidiu Cristinel Stoica and published by Minkowski Institute Press. This book was released on 2015-04-21 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Book Synopsis Statistical Theory and Method Abstracts by :
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 2001 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
