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Author : Svetlozar Todorov Rachev
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.3/5 (121 download)
Download or read book Duality Theorems for Kantorovich-Rubinstein and Wasserstein Functionals written by Svetlozar Todorov Rachev and published by . This book was released on 1990 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147044738X
Total Pages : 286 pages
Book Rating : 4.4/5 (74 download)
Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.
Author : Ştefan Cobzaş
Publisher : Springer
ISBN 13 : 3030164896
Total Pages : 605 pages
Book Rating : 4.0/5 (31 download)
Download or read book Lipschitz Functions written by Ştefan Cobzaş and published by Springer. This book was released on 2019-05-23 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Author : Svetlozar T. Rachev
Publisher : Springer Science & Business Media
ISBN 13 : 1461448697
Total Pages : 616 pages
Book Rating : 4.4/5 (614 download)
Download or read book The Methods of Distances in the Theory of Probability and Statistics written by Svetlozar T. Rachev and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)
Author : Svetlozar T. Rachev
Publisher : Springer Science & Business Media
ISBN 13 : 0387227563
Total Pages : 450 pages
Book Rating : 4.3/5 (872 download)
Download or read book Mass Transportation Problems written by Svetlozar T. Rachev and published by Springer Science & Business Media. This book was released on 2006-05-09 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.
Author : Luis A. Caffarelli
Publisher : American Mathematical Soc.
ISBN 13 : 0821809172
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)
Download or read book Monge Ampere Equation: Applications to Geometry and Optimization written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1999 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Monge Ampère Equation has received attention for its role in several new areas of applied mathematics: as a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc.; as a simple model for optimal transportation and a div-curl decomposition with affine invariance; and as a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.
Author : Henryk Gacki
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.0/5 ( download)
Download or read book Applications of the Kantorovich-Rubinstein Maximum Principle in the Theory of Markov Semigroups written by Henryk Gacki and published by . This book was released on 2007 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yingmin Jia
Publisher : Springer Nature
ISBN 13 : 9811663203
Total Pages : 866 pages
Book Rating : 4.8/5 (116 download)
Download or read book Proceedings of 2021 Chinese Intelligent Systems Conference written by Yingmin Jia and published by Springer Nature. This book was released on 2021-10-06 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 17th Chinese Intelligent Systems Conference, held in Fuzhou, China, on Oct 16-17, 2021. It focuses on new theoretical results and techniques in the field of intelligent systems and control. This is achieved by providing in-depth study on a number of major topics such as Multi-Agent Systems, Complex Networks, Intelligent Robots, Complex System Theory and Swarm Behavior, Event-Triggered Control and Data-Driven Control, Robust and Adaptive Control, Big Data and Brain Science, Process Control, Intelligent Sensor and Detection Technology, Deep learning and Learning Control Guidance, Navigation and Control of Flight Vehicles and so on. The book is particularly suited for readers who are interested in learning intelligent system and control and artificial intelligence. The book can benefit researchers, engineers, and graduate students.
Author : Leszek Rutkowski
Publisher : Springer
ISBN 13 : 3030209121
Total Pages : 688 pages
Book Rating : 4.0/5 (32 download)
Download or read book Artificial Intelligence and Soft Computing written by Leszek Rutkowski and published by Springer. This book was released on 2019-05-27 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 11508 and 11509 constitutes the refereed proceedings of of the 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019, held in Zakopane, Poland, in June 2019. The 122 revised full papers presented were carefully reviewed and selected from 333 submissions. The papers included in the first volume are organized in the following five parts: neural networks and their applications; fuzzy systems and their applications; evolutionary algorithms and their applications; pattern classification; artificial intelligence in modeling and simulation. The papers included in the second volume are organized in the following five parts: computer vision, image and speech analysis; bioinformatics, biometrics, and medical applications; data mining; various problems of artificial intelligence; agent systems, robotics and control.
Author : Victor M. Panaretos
Publisher : Springer Nature
ISBN 13 : 3030384381
Total Pages : 157 pages
Book Rating : 4.0/5 (33 download)
Download or read book An Invitation to Statistics in Wasserstein Space written by Victor M. Panaretos and published by Springer Nature. This book was released on 2020-03-10 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
Author : Kęstutis Kubilius
Publisher : Springer
ISBN 13 : 3319710303
Total Pages : 390 pages
Book Rating : 4.3/5 (197 download)
Download or read book Parameter Estimation in Fractional Diffusion Models written by Kęstutis Kubilius and published by Springer. This book was released on 2018-01-04 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.
Author : Cédric Villani
Publisher : American Mathematical Soc.
ISBN 13 : 1470467267
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topics in Optimal Transportation written by Cédric Villani and published by American Mathematical Soc.. This book was released on 2021-08-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.
Author :
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.X/5 (2 download)
Download or read book Probability and Mathematical Statistics written by and published by . This book was released on 1992 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Daniel Mauldin
Publisher : American Mathematical Soc.
ISBN 13 : 0821850997
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)
Download or read book Measure and Measurable Dynamics written by R. Daniel Mauldin and published by American Mathematical Soc.. This book was released on 1989 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dorothy Maharam Stone's contributions to operators and measure algebras has had a profound influence on this area of research. This volume contains the proceedings of the Conference on Measure and Measurable Dynamics, held in honor of Stone at the University of Rochester in September 1987.
Author : Society for Industrial and Applied Mathematics
Publisher :
ISBN 13 :
Total Pages : 960 pages
Book Rating : 4.:/5 (318 download)
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 1994 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hulin Wu
Publisher : CRC Press
ISBN 13 : 1000260968
Total Pages : 268 pages
Book Rating : 4.0/5 (2 download)
Download or read book Statistics and Machine Learning Methods for EHR Data written by Hulin Wu and published by CRC Press. This book was released on 2020-12-10 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Electronic Health Records (EHR)/Electronic Medical Records (EMR) data is becoming more prevalent for research. However, analysis of this type of data has many unique complications due to how they are collected, processed and types of questions that can be answered. This book covers many important topics related to using EHR/EMR data for research including data extraction, cleaning, processing, analysis, inference, and predictions based on many years of practical experience of the authors. The book carefully evaluates and compares the standard statistical models and approaches with those of machine learning and deep learning methods and reports the unbiased comparison results for these methods in predicting clinical outcomes based on the EHR data. Key Features: Written based on hands-on experience of contributors from multidisciplinary EHR research projects, which include methods and approaches from statistics, computing, informatics, data science and clinical/epidemiological domains. Documents the detailed experience on EHR data extraction, cleaning and preparation Provides a broad view of statistical approaches and machine learning prediction models to deal with the challenges and limitations of EHR data. Considers the complete cycle of EHR data analysis. The use of EHR/EMR analysis requires close collaborations between statisticians, informaticians, data scientists and clinical/epidemiological investigators. This book reflects that multidisciplinary perspective.
Author : Cédric Villani
Publisher : Springer Science & Business Media
ISBN 13 : 3540710507
Total Pages : 970 pages
Book Rating : 4.5/5 (47 download)
Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
