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Limit Theorems for Stochastic Processes

Author: Jean Jacod

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 620

ISBN-13: 3662025140

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.

Limit Theorems for Randomly Stopped Stochastic Processes

Author: Dmitrii S. Silvestrov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 408

ISBN-13: 0857293907

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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.

Limit Theorems for Randomly Stopped Stochastic Processes

Author: Dimitri Silvestrov

Publisher:

Published: 2014-01-15

Total Pages: 416

ISBN-13: 9780857293916

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Stochastic-Process Limits

Author: Ward Whitt

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 616

ISBN-13: 0387217487

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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

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Author:

Publisher:

Published: 1909

Total Pages:

ISBN-13:

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Convergence of Stochastic Processes

Author: D. Pollard

Publisher: David Pollard

Published: 1984-10-08

Total Pages: 223

ISBN-13: 0387909907

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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Limit Theorems on Large Deviations for Markov Stochastic Processes

Author: A.D. Wentzell

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 192

ISBN-13: 9400918526

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In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum - the distribution of the value of a stochastic process at one (time) point - or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.

Weak Convergence of Stochastic Processes

Author: Vidyadhar S. Mandrekar

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2016-09-26

Total Pages: 148

ISBN-13: 3110475456

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The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents: Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography

Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness

Author: Hubert Hennion

Publisher: Springer Science & Business Media

Published: 2001-08

Total Pages: 150

ISBN-13: 3540424156

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This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.

Stochastic Limit Theory

Author: Arnold I. Davidson

Publisher: Oxford University Press

Published: 1994

Total Pages: 562

ISBN-13: 0198774036

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This major new econometrics text surveys recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. Designed for econometricians and advanced students with limited mathematical training, the book clearly lays out the necessary math and probability theory and uses numerous examples to make its data useful and comprehensible. It also includes original new material from Davidson's own research on central limit theorems. About the Series Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.