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Approximation Probability And Related Fields
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Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :1461524946 Total Pages :441 pages Book Rating :4.4/5 (615 download)
Book Synopsis Approximation, Probability, and Related Fields by : George A. Anastassiou
Download or read book Approximation, Probability, and Related Fields written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a conference held in Santa Barbara, California, May 20-22, 1993
Book Synopsis Quantitative Approximations by : George Anastassiou
Download or read book Quantitative Approximations written by George Anastassiou and published by CRC Press. This book was released on 2000-09-15 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.
Book Synopsis Normal Approximation by Stein’s Method by : Louis H.Y. Chen
Download or read book Normal Approximation by Stein’s Method written by Louis H.Y. Chen and published by Springer Science & Business Media. This book was released on 2010-10-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Book Synopsis Quantitative Approximations by : George A. Anastassiou
Download or read book Quantitative Approximations written by George A. Anastassiou and published by Chapman and Hall/CRC. This book was released on 2000 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert.Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers.The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.
Book Synopsis Probability Approximations and Beyond by : Andrew Barbour
Download or read book Probability Approximations and Beyond written by Andrew Barbour and published by Springer Science & Business Media. This book was released on 2011-12-07 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Book Synopsis An Introduction to Stein's Method by : A. D. Barbour
Download or read book An Introduction to Stein's Method written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Book Synopsis Foundations of Modern Probability by : Olav Kallenberg
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Book Synopsis Research Developments in Probability And Statistics by : Madan Lal Puri
Download or read book Research Developments in Probability And Statistics written by Madan Lal Puri and published by VSP. This book was released on 1996-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the 65th birthday of Professor Madan L. Puri, the authors of this Festschrift pay their tribute to his scientific achievements in statistics. This volume reflects a selective survey of leading contemprary scientific trends and developments that are significantly related to ideas expressed and pursued in Madan L. Puri's work in statistics and related fields. The wide spectrum of scientific interest which characterizes Professor Puri's scientific activity is thus illuminated. The choice of papers offered combines fundamental principles with interesting applications, selected for their originality and insight, and for their influence on the modern approach to statistics, probability and related fields.
Book Synopsis Asymptotic Approximations for Probability Integrals by : Karl W. Breitung
Download or read book Asymptotic Approximations for Probability Integrals written by Karl W. Breitung and published by Springer. This book was released on 2006-11-14 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Book Synopsis Approximation Problems in Analysis and Probability by : M.P. Heble
Download or read book Approximation Problems in Analysis and Probability written by M.P. Heble and published by Elsevier. This book was released on 2011-08-18 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney's theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞-approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.
Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona
Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona and published by Springer. This book was released on 2018-03-08 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Book Synopsis Advances in Summability and Approximation Theory by : S. A. Mohiuddine
Download or read book Advances in Summability and Approximation Theory written by S. A. Mohiuddine and published by Springer. This book was released on 2018-12-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
Book Synopsis Moments in Probability and Approximation Theory by : George Anastassiou
Download or read book Moments in Probability and Approximation Theory written by George Anastassiou and published by Chapman and Hall/CRC. This book was released on 1993-04-19 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique volume covering the author's research over the last decade in this exciting area.
Book Synopsis Information-Theoretic Methods for Estimating of Complicated Probability Distributions by : Zhi Zong
Download or read book Information-Theoretic Methods for Estimating of Complicated Probability Distributions written by Zhi Zong and published by Elsevier. This book was released on 2006-08-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC
Book Synopsis Functional and High-Dimensional Statistics and Related Fields by : Germán Aneiros
Download or read book Functional and High-Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer Nature. This book was released on 2020-06-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.
Book Synopsis High Dimensional Probability IX by : Radosław Adamczak
Download or read book High Dimensional Probability IX written by Radosław Adamczak and published by Springer Nature. This book was released on 2023-06-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
Download or read book Mathematical Reviews written by and published by . This book was released on 1995 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
