Download or read book Limit Theorems for Infinitely Divisible Random Fields written by Aurel Kleinerman and published by . This book was released on 1977 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Associated Random Fields and Related Systems written by Aleksandr Vadimovich Bulinski? and published by World Scientific. This book was released on 2007 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
Download or read book Limit Theorems for Associated Random Fields and Related Systems written by Aleksandr Vadimovich Bulinskii and published by World Scientific. This book was released on 2007 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications. There are 434 items in the bibliography. The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.). Contents: Random Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.
Download or read book Uniform Limit Theorems for Sums of Independent Random Variables written by Taĭvo Viktorovich Arak and published by American Mathematical Soc.. This book was released on 1988 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. This book presents a study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions.
Download or read book Limit Theorems in Probability Theory and Related Fields written by and published by . This book was released on 1987 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Stein s Method for Infinitely Divisible Laws with Finite First Moment written by Benjamin Arras and published by Springer. This book was released on 2019-04-26 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantitative approximation results for weak limit theorems when the target limiting law is infinitely divisible with finite first moment. Two methods are presented and developed to obtain such quantitative results. At the root of these methods stands a Stein characterizing identity discussed in the third chapter and obtained thanks to a covariance representation of infinitely divisible distributions. The first method is based on characteristic functions and Stein type identities when the involved sequence of random variables is itself infinitely divisible with finite first moment. In particular, based on this technique, quantitative versions of compound Poisson approximation of infinitely divisible distributions are presented. The second method is a general Stein's method approach for univariate selfdecomposable laws with finite first moment. Chapter 6 is concerned with applications and provides general upper bounds to quantify the rate of convergence in classical weak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.
Download or read book Limit Theorems for the Distributions of the Maxima of Partial Sums of Independent Random Variables written by Ernest G. Kimme and published by . This book was released on 1957 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Random Fields written by Nguyen Van Thu and published by . This book was released on 1981 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nicolai Leonenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.
Download or read book Limit Theorems in Probability and Statistics written by Pál Révész and published by Elsevier Science & Technology. This book was released on 1984 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Limit Theorem and the Distribution of the Stochastic Integral written by D. L. Clark and published by . This book was released on 1957 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Parts of Random Variables written by Roeland Joannes Gerardus Wilms and published by . This book was released on 1994 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nikolai Leonenko and published by Springer. This book was released on 2011-09-29 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dependence and Limit Theorems for Stationary Infinitely Divisible Sequences written by Dyana Rae Harrelson and published by . This book was released on 2000 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Multi Indexed Sums of Random Variables written by Oleg Klesov and published by Springer. This book was released on 2014-10-13 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.
Download or read book Limit Theorems for Large Deviations written by L. Saulis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series
Download or read book Limit Theorems and Some Applications in Statistical Physics written by Boris Nahapetian and published by Springer. This book was released on 1991-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
