Central Limit Theorems For Set Indexed Strong Martingales
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Central Limit Theorems For Set Indexed Strong Martingales
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Author :
language : en
Publisher:
Release Date : 1998
Central Limit Theorems For Set Indexed Strong Martingales written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Set Indexed Martingales
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Author : B.G. Ivanoff
language : en
Publisher: CRC Press
Release Date : 1999-10-27
Set Indexed Martingales written by B.G. Ivanoff and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-27 with Mathematics categories.
Set-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved. Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.
Conditional Lindeberg Central Limit Theorem For Strong Lattice Martingales
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Author : Illig Aude
language : en
Publisher:
Release Date : 2018
Conditional Lindeberg Central Limit Theorem For Strong Lattice Martingales written by Illig Aude and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Strong lattice martingale arrays over Z are considered under the form of set-indexed processes and a central limit theorem is established under conditional Lindeberg condition, after having extended the limit theorem in Tjostheim (1983) to spatial processes that are nearly lattice martingales.
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.
Topics In Spatial Stochastic Processes
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Author : Vincenzo Capasso
language : en
Publisher: Springer
Release Date : 2003-01-01
Topics In Spatial Stochastic Processes written by Vincenzo Capasso and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.
Limit Theorems For Multi Indexed Sums Of Random Variables
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Author : Oleg Klesov
language : en
Publisher: Springer
Release Date : 2014-10-13
Limit Theorems For Multi Indexed Sums Of Random Variables written by Oleg Klesov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
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.
Martingale Approximations
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Author : I︠U︡riĭ Vasilʹevich Borovskikh
language : en
Publisher: VSP
Release Date : 1997
Martingale Approximations written by I︠U︡riĭ Vasilʹevich Borovskikh and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
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.
Uniform Central Limit Theorems
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Author : R. M. Dudley
language : en
Publisher: Cambridge University Press
Release Date : 2014-02-24
Uniform Central Limit Theorems written by R. M. Dudley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-24 with Mathematics categories.
This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 1999
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Dissertations, Academic categories.