Download or read book U Statistics in Banach Spaces written by IU. IUrii Vasilevich Borovskikh and published by VSP. This book was released on 1996-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: U-statistics are universal objects of modern probabilistic summation theory. They appear in various statistical problems and have very important applications. The mathematical nature of this class of random variables has a functional character and, therefore, leads to the investigation of probabilistic distributions in infinite-dimensional spaces. The situation when the kernel of a U-statistic takes values in a Banach space, turns out to be the most natural and interesting. In this book, the author presents in a systematic form the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), which has been developed to date. The exposition of the material in this book is based around the following topics: algebraic and martingale properties of U-statistics; inequalities; law of large numbers; the central limit theorem; weak convergence to a Gaussian chaos and multiple stochastic integrals; invariance principle and functional limit theorems; estimates of the rate of weak convergence; asymptotic expansion of distributions; large deviations; law of iterated logarithm; dependent variables; relation between Banach-valued U-statistics and functionals from permanent random measures.

Download or read book U Statistics in Banach Spaces written by Yu. V. Borovskikh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "U-Statistics in Banach Spaces".

Download or read book Selected Works of R M Dudley written by Evarist Giné and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. His work on Gaussian processes led to the understanding of the basic fact that their sample boundedness and continuity should be characterized in terms of proper measures of complexity of their parameter spaces equipped with the intrinsic covariance metric. His sufficient condition for sample continuity in terms of metric entropy is widely used and was proved by X. Fernique to be necessary for stationary Gaussian processes, whereas its more subtle versions (majorizing measures) were proved by M. Talagrand to be necessary in general. Together with V. N. Vapnik and A. Y. Cervonenkis, R. M. Dudley is a founder of the modern theory of empirical processes in general spaces. His work on uniform central limit theorems (under bracketing entropy conditions and for Vapnik-Cervonenkis classes), greatly extends classical results that go back to A. N. Kolmogorov and M. D. Donsker, and became the starting point of a new line of research, continued in the work of Dudley and others, that developed empirical processes into one of the major tools in mathematical statistics and statistical learning theory. As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm. In a further recent step Dudley replaces this norm by the stronger p-variation norms, which then allows replacing compact differentiability of many statistical functionals by Fréchet differentiability in the delta method. Richard M. Dudley has also made important contributions to mathematical statistics, the theory of weak convergence, relativistic Markov processes, differentiability of nonlinear operators and several other areas of mathematics. Professor Dudley has been the adviser to thirty PhD's and is a Professor of Mathematics at the Massachusetts Institute of Technology.

Download or read book Uniform Central Limit Theorems written by R. M. Dudley and published by Cambridge University Press. This book was released on 1999-07-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise by an acknowledged expert includes several topics not found in any previous book.

Download or read book Probability Theory Subject Indexes from Mathematical Reviews written by American Mathematical Society and published by . This book was released on 1987 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Dependence in Probability and Statistics written by Eberlein and published by Birkhäuser. This book was released on 1986 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Mathematics of Operations Research written by and published by . This book was released on 1988 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles of mathematical interest as well as operations research and management science.

Download or read book Index of Mathematical Papers written by and published by . This book was released on 1973 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Martingales in Banach Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2016-06-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.

Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Download or read book Current Index to Statistics Applications Methods and Theory written by and published by . This book was released on 1996 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.

Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.

Download or read book Comprehensive Dissertation Index Mathematics Statistics Physics A E written by and published by . This book was released on 1984 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: