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Central Limit Theory For Martingales Via Random Change Of Time
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Author :Dmitrii S. Silvestrov Publisher :Springer Science & Business Media ISBN 13 :0857293907 Total Pages :408 pages Book Rating :4.8/5 (572 download)
Book Synopsis Limit Theorems for Randomly Stopped Stochastic Processes by : Dmitrii S. Silvestrov
Download or read book Limit Theorems for Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Book Synopsis Martingale Approximations by : I︠U︡riĭ Vasilʹevich Borovskikh
Download or read book Martingale Approximations written by I︠U︡riĭ Vasilʹevich Borovskikh and published by VSP. This book was released on 1997 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.
Book Synopsis Stable Convergence and Stable Limit Theorems by : Erich Häusler
Download or read book Stable Convergence and Stable Limit Theorems written by Erich Häusler and published by Springer. This book was released on 2015-06-09 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Book Synopsis Probability: A Graduate Course by : Allan Gut
Download or read book Probability: A Graduate Course written by Allan Gut and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.
Download or read book Probability written by Allan Gut and published by Springer Science & Business Media. This book was released on 2013 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
Book Synopsis Limit Theorems For Nonlinear Cointegrating Regression by : Qiying Wang
Download or read book Limit Theorems For Nonlinear Cointegrating Regression written by Qiying Wang and published by World Scientific. This book was released on 2015-07-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the limit theorems that can be used in the development of nonlinear cointegrating regression. The topics include weak convergence to a local time process, weak convergence to a mixture of normal distributions and weak convergence to stochastic integrals. This book also investigates estimation and inference theory in nonlinear cointegrating regression.The core context of this book comes from the author and his collaborator's current researches in past years, which is wide enough to cover the knowledge bases in nonlinear cointegrating regression. It may be used as a main reference book for future researchers.
Book Synopsis Martingale Limit Theory and Its Application by : P. Hall
Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probability and Mathematical Statistics by : Allan Gut
Download or read book Probability and Mathematical Statistics written by Allan Gut and published by . This book was released on 1983 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A History of the Central Limit Theorem by : Hans Fischer
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Book Synopsis Fluctuations in Markov Processes by : Tomasz Komorowski
Download or read book Fluctuations in Markov Processes written by Tomasz Komorowski and published by Springer Science & Business Media. This book was released on 2012-07-05 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Book Synopsis Limit Theorems for Stochastic Processes by : Jean Jacod
Download or read book Limit Theorems for Stochastic Processes written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Book Synopsis Weakly Dependent Stochastic Sequences and Their Applications: Summation theory for weakly dependent sequences by : Ken-ichi Yoshihara
Download or read book Weakly Dependent Stochastic Sequences and Their Applications: Summation theory for weakly dependent sequences written by Ken-ichi Yoshihara and published by . This book was released on 1992 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dependence in Probability and Statistics by : Eberlein
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:
Book Synopsis Mathematics of Operations Research by :
Download or read book Mathematics of Operations Research written by and published by . This book was released on 1990 with total page 892 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 Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Book Synopsis Stochastic-Process Limits by : Ward Whitt
Download or read book Stochastic-Process Limits written by Ward Whitt and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
