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Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers i
Distribution (Probability theory) --- Approximation theory --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities
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Distributed and communicating objects are becoming ubiquitous. In global, Grid and Peer-to-Peer computing environments, extensive use is made of objects interacting through method calls. So far, no general formalism has been proposed for the foundation of such systems. Caromel and Henrio are the first to define a calculus for distributed objects interacting using asynchronous method calls with generalized futures, i.e., wait-by-necessity -- a must in large-scale systems, providing both high structuring and low coupling, and thus scalability. The authors provide very generic results on expressiveness and determinism, and the potential of their approach is further demonstrated by its capacity to cope with advanced issues such as mobility, groups, and components. Researchers and graduate students will find here an extensive review of concurrent languages and calculi, with comprehensive figures and summaries. Developers of distributed systems can adopt the many implementation strategies that are presented and analyzed in detail. Preface by Luca Cardelli.
Distribution (Probability theory) --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Programming --- Computer architecture. Operating systems
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This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.
Stochastic processes --- Distribution (Probability theory) --- 519.2 --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical Sciences --- Probability
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The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Stochastic differential equations. --- Differential equations --- Fokker-Planck equation
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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
Distribution (Probability theory) --- Approximation theory. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities
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Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (available separately or together as a Set), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician.
517.98 --- 519.213 --- 517.91 --- 517.91 Ordinary differential equations: general theory --- Ordinary differential equations: general theory --- 519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Mathematical analysis. --- Analyse fonctionnelle --- Functional analysis --- Fonctions d'une variable réelle
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Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.
Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Distribution (Probability theory. --- Mathematics. --- Probability Theory and Stochastic Processes. --- Operations Research, Management Science. --- Mathematics, general. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Operations research. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory
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This is the first comprehensive treatment of the three basic symmetries of probability theory—contractability, exchangeability, and rotatability—defined as invariance in distribution under contractions, permutations, and rotations. Originating with the pioneering work of de Finetti from the 1930's, the theory has evolved into a unique body of deep, beautiful, and often surprising results, comprising the basic representations and invariance properties in one and several dimensions, and exhibiting some unexpected links between the various symmetries as well as to many other areas of modern probability. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book. Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991–94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.
Probabilities. --- Symmetry (Physics) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Conservation laws (Physics) --- Physics --- Mathematical statistics. --- Distribution (Probability theory. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics
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From the reviews "[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, on a technically difficult subject, makes a fascinating subject and its open problem as accessible as possible. [...]F.L. Spitzer in Mathematical Reviews, 1986 " [...] This book, the first monographic presentation of this important and rapidly developing theory, will prove indispensable to every serious student of stochastics [...]" S. Gacsályi in Publicationes Mathematicae, 1986 "[...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...]" G. Rosenkranz in Methods of Information in Medicine, 1986.
Stochastic processes. --- Mathematical physics. --- Biomathematics. --- Biology --- Mathematics --- Physical mathematics --- Physics --- Random processes --- Probabilities --- Distribution (Probability theory. --- Statistical physics. --- Probability Theory and Stochastic Processes. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Mathematical statistics --- Statistical methods --- Probabilities. --- Dynamical systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk
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A problem of broad interest – the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) – is covered in this book. The area has a wide range of applications, and provides a tool to describe the phase transitions and the effectiveness of random algorithms. In particular, the book studies a subset of the general problem, taking some approaches that have, up till now, only appeared largely in the Chinese literature. Eigenvalues, Inequalities and Ergodic Theory serves as an introduction to this developing field, and provides an overview of the methods used, in an accessible and concise manner. The author starts with an overview chapter, from which any of the following self-contained chapters can be read. Each chapter starts with a summary and, in order to appeal to non-specialists, ideas are introduced through simple examples rather than technical proofs. In the latter chapters readers are introduced to problems and application areas, including stochastic models of economy. Intended for researchers, graduates and postgraduates in probability theory, Markov processes, mathematical physics and spectrum theory, this book will be a welcome introduction to a growing area of research.
Eigenvalues. --- Inequalities (Mathematics) --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Processes, Infinite --- Matrices --- Probability theory --- Distribution (Probability theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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