Martingale Limit Theory
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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.
Martingale Approximation
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Author : Yu. V. Borovskikh
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-01-14
Martingale Approximation written by Yu. V. Borovskikh 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 2019-01-14 with Mathematics categories.
No detailed description available for "Martingale Approximation".
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.
Limit Theorems For Stochastic Processes
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Limit Theorems For Stochastic Processes written by Jean Jacod 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 2013-03-09 with Mathematics categories.
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.
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.
The Convergence Of Moments In The Martingale Central Limit Theorem
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Author : Peter Hall
language : en
Publisher:
Release Date : 1978
The Convergence Of Moments In The Martingale Central Limit Theorem written by Peter Hall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Central limit theorem categories.
Some Remarks On The Martingale Central Limit Theorem
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Author : Esbjörn Ohlsson
language : en
Publisher:
Release Date : 1985
Some Remarks On The Martingale Central Limit Theorem written by Esbjörn Ohlsson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Central Limit Theory For Martingales Via Random Change Of Time
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Author : Holger Rootzén
language : en
Publisher:
Release Date : 1983
Central Limit Theory For Martingales Via Random Change Of Time written by Holger Rootzén and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
This paper contains an exposition of the by now rather complete central limit theory for discrete parameter martingales providing new and efficient proofs. The basic idea is to start by proving a central limit theorem under quite restrictive conditions (that the summands tend uniformly to zero and that the sums of squares converge uniformly) and then to obtain the most general results by random change of time and truncation. The emphasis is on the sums of squares (or squared variation process), and Burkholder's square function inequality plays a crucial role in the development. In particular, this approach leads to a very short and direct proof of tightness. In the proofs we make much use of a result which is believed to be new and which binds together convergence to zero of sums and of sums of conditional expectations. In the final section, the results are extended to several dimensions, to mixing convergence, and to convergence to mixtures of normal distributions. (Author).
Problems In Limit Theory For Martingales And Posterior Distributions From Stochastic Processes
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Author : Iain Murray Johnstone
language : en
Publisher:
Release Date : 1978
Problems In Limit Theory For Martingales And Posterior Distributions From Stochastic Processes written by Iain Murray Johnstone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Limit theorems (Probability theory) categories.