Martingale Limit Theory And Its Application

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Martingale Limit Theory and Its Application

Author : P. Hall
Publisher : Academic Press
ISBN 13 : 1483263223
Total Pages : 321 pages
Book Rating : 4.4/5 (832 download)

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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.

Modern Probability Theory

Author : B. Ramdas Bhat
Publisher : New Age International
ISBN 13 : 9788122411898
Total Pages : 348 pages
Book Rating : 4.4/5 (118 download)

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Book Synopsis Modern Probability Theory by : B. Ramdas Bhat

Download or read book Modern Probability Theory written by B. Ramdas Bhat and published by New Age International. This book was released on 2007 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Book Continues To Cover The Syllabus Of A One-Year Course On Probability Theory. The Rigorous Axiomatic Approach Continues To Be Followed. For Those Who Plan To Apply Probability Models In Their Chosen Areas The Book Will Provide The Necessary Foundation. For Those Who Want To Proceed To Work In The Area Of Stochastic Processes, The Present Work Will Provide The Necessary Preliminary Background. It Can Be Used By Probabilists, Statisticians And Mathematicians. In The Present Revised Edition Many Concepts Have Been Elaborated. Clarifications Are Given For A Number Of Steps In The Proofs Of Results Derived. Additional Examples And Problems Are Given At The End Of Different Chapters. An Additional Preliminary Chapter Has Been Added So That Students Can Recapitulate The Topics Normally Covered In The Undergraduate Courses. It Also Forms The Foundation For Topics Covered In The Remaining Chapters. The Third Edition Incorporates The Suggestions For Improvements Received By The Author When The Earlier Editions Were In Circulation. With The Additional Features And Most Of The Errors Weeded Out, The Book Is Hoped To Become More Useful In The Hands Of Students And Teachers.

Martingale Limit Theory

Author : Peter Gavin Hall
Publisher :
ISBN 13 :
Total Pages : 93 pages
Book Rating : 4.:/5 (222 download)

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Book Synopsis Martingale Limit Theory by : Peter Gavin Hall

Download or read book Martingale Limit Theory written by Peter Gavin Hall and published by . This book was released on 1975 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Limit Theory

Author : James Davidson
Publisher : Oxford University Press
ISBN 13 : 0192658808
Total Pages : 796 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Stochastic Limit Theory by : James Davidson

Download or read book Stochastic Limit Theory written by James Davidson and published by Oxford University Press. This book was released on 2021-11-04 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Limit Theory, published in 1994, has become a standard reference in its field. Now reissued in a new edition, offering updated and improved results and an extended range of topics, Davidson surveys asymptotic (large-sample) distribution theory with applications to econometrics, with particular emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First, as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration. The new edition gives updated and improved versions of many of the results and extends the coverage of many topics, in particular the theory of convergence to alpha-stable limits of processes with infinite variance.

Weak Convergence and Its Applications

Author : Zhengyan Lin
Publisher : World Scientific
ISBN 13 : 9814447706
Total Pages : 185 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Weak Convergence and Its Applications by : Zhengyan Lin

Download or read book Weak Convergence and Its Applications written by Zhengyan Lin and published by World Scientific. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory.Contents: "The Definition and Basic Properties of Weak Convergence: "Metric SpaceThe Definition of Weak Convergence of Stochastic Processes and Portmanteau TheoremHow to Verify the Weak Convergence?Two Examples of Applications of Weak Convergence"Convergence to the Independent Increment Processes: "The Basic Conditions of Convergence to the Gaussian Independent Increment ProcessesDonsker Invariance PrincipleConvergence of Poisson Point ProcessesTwo Examples of Applications of Point Process Method"Convergence to Semimartingales: "The Conditions of Tightness for Semimartingale SequenceWeak Convergence to SemimartingaleWeak Convergence to Stochastic Integral I: The Martingale Convergence ApproachWeak Convergence to Stochastic Integral II: Kurtz and Protter's ApproachStable Central Limit Theorem for SemimartingalesAn Application to Stochastic Differential EquationsAppendix: The Predictable Characteristics of Semimartingales"Convergence of Empirical Processes: "Classical Weak Convergence of Empirical ProcessesWeak Convergence of Marked Empirical ProcessesWeak Convergence of Function Index Empirical ProcessesWeak Convergence of Empirical Processes Involving Time-Dependent dataTwo Examples of Applications in Statistics Readership: Graduate students and researchers in probability & statistics and econometrics.

Stochastic Processes: Basic Theory And Its Applications

Author : Narahari U Prabhu
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106956
Total Pages : 356 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Stochastic Processes: Basic Theory And Its Applications by : Narahari U Prabhu

Download or read book Stochastic Processes: Basic Theory And Its Applications written by Narahari U Prabhu and published by World Scientific Publishing Company. This book was released on 2007-10-02 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.

Theory of Martingales

Author : Robert Liptser
Publisher : Springer Science & Business Media
ISBN 13 : 9400924380
Total Pages : 806 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Theory of Martingales by : Robert Liptser

Download or read book Theory of Martingales written by Robert Liptser and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities 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'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

Probability Theory and Applications

Author :
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112314220
Total Pages : 820 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis Probability Theory and Applications by :

Download or read book Probability Theory and Applications written by and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probability Theory and Applications".

Limit Theorems for Stochastic Processes

Author : Jean Jacod
Publisher : Springer Science & Business Media
ISBN 13 : 3662025140
Total Pages : 620 pages
Book Rating : 4.6/5 (62 download)

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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.

Probability Theory with Applications

Author : M. M. Rao
Publisher : Elsevier
ISBN 13 : 0080925367
Total Pages : 510 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Probability Theory with Applications by : M. M. Rao

Download or read book Probability Theory with Applications written by M. M. Rao and published by Elsevier. This book was released on 1984-02-01 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material in this book is designed for a standard graduate course on probability theory, including some important applications. It was prepared from the sets of lecture notes for a course that I have taught several times over the past 20 years. The present version reflects the reactions of my audiences as well as some of the textbooks that I used.

Functional Gaussian Approximation for Dependent Structures

Author : Florence Merlevède
Publisher : Oxford University Press
ISBN 13 : 0192561863
Total Pages : 496 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Functional Gaussian Approximation for Dependent Structures by : Florence Merlevède

Download or read book Functional Gaussian Approximation for Dependent Structures written by Florence Merlevède and published by Oxford University Press. This book was released on 2019-02-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.

Semimartingales and their Statistical Inference

Author : B.L.S. Prakasa Rao
Publisher : Routledge
ISBN 13 : 1351416928
Total Pages : 247 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Semimartingales and their Statistical Inference by : B.L.S. Prakasa Rao

Download or read book Semimartingales and their Statistical Inference written by B.L.S. Prakasa Rao and published by Routledge. This book was released on 2019-01-15 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.

A Central Limit Theorem for $ \ell^ \infty $ -valued Martingale Difference Arrays and Its Application

$Download A Central Limit Theorem for $ \ell^ \infty $ -valued Martingale Difference Arrays and Its Application PDF Online Free$

Author : Y. Nishiyama
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis A Central Limit Theorem for $ \ell^ \infty $ -valued Martingale Difference Arrays and Its Application by : Y. Nishiyama

Download or read book A Central Limit Theorem for $ \ell^ \infty $ -valued Martingale Difference Arrays and Its Application written by Y. Nishiyama and published by . This book was released on 1996 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability Theory

Author : Yuan Shih Chow
Publisher : Springer Science & Business Media
ISBN 13 : 1461219507
Total Pages : 505 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Probability Theory by : Yuan Shih Chow

Download or read book Probability Theory written by Yuan Shih Chow and published by Springer Science & Business Media. This book was released on 2012-11-28 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: - A comprehensive treatment of the law of the iterated logarithm - The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof - Development and applications of the second moment analogue of Walds equation - Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem - Complete discussion, including central limit theorem, of the random casting of r balls into n cells - Recent martingale inequalities - Cram r-L vy theorem and factor-closed families of distributions.

Probability with Martingales

Author : David Williams
Publisher : Cambridge University Press
ISBN 13 : 9780521406055
Total Pages : 274 pages
Book Rating : 4.4/5 (6 download)

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Book Synopsis Probability with Martingales by : David Williams

Download or read book Probability with Martingales written by David Williams and published by Cambridge University Press. This book was released on 1991-02-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.

The New Palgrave Dictionary of Economics

Author :
Publisher : Springer
ISBN 13 : 1349588024
Total Pages : 7493 pages
Book Rating : 4.3/5 (495 download)

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Book Synopsis The New Palgrave Dictionary of Economics by :

Download or read book The New Palgrave Dictionary of Economics written by and published by Springer. This book was released on 2016-05-18 with total page 7493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product.

Probability Theory III

Author : Yurij V. Prokhorov
Publisher : Springer Science & Business Media
ISBN 13 : 3662036401
Total Pages : 260 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Probability Theory III by : Yurij V. Prokhorov

Download or read book Probability Theory III written by Yurij V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.