Martingale Limit Theory And Its Application
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Martingale Limit Theory And Its Application
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Author : P. Hall
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Martingale Limit Theory And Its Application written by P. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
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.
Martingale Limit Theory
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Author : Peter Gavin Hall
language : en
Publisher:
Release Date : 1975
Martingale Limit Theory written by Peter Gavin Hall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Martingales (Mathematics) categories.
Modern Probability Theory
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Author : B. Ramdas Bhat
language : en
Publisher: New Age International
Release Date : 2007
Modern Probability Theory written by B. Ramdas Bhat and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Probabilities categories.
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.
Probability Theory
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Author : Yuan Shih Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-28
Probability Theory written by Yuan Shih Chow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-28 with Mathematics categories.
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.
Stopped Random Walks
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stopped Random Walks written by Allan Gut and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words.
Weak Convergence And Its Applications
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Author : Zhengyan Lin
language : en
Publisher: World Scientific
Release Date : 2014
Weak Convergence And Its Applications written by Zhengyan Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Business & Economics categories.
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 Limit Theory
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Author : James Davidson
language : en
Publisher: OUP Oxford
Release Date : 1994-10-13
Stochastic Limit Theory written by James Davidson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-13 with Business & Economics categories.
This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory, with a special 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, including a number of important new results. 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.
Stochastic Processes
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Author : Narahari U Prabhu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-10-02
Stochastic Processes written by Narahari U Prabhu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-02 with Mathematics categories.
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
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Author : Robert Liptser
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Martingales written by Robert Liptser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
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Author :
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Probability Theory And Applications written by and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
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