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Author : Marc Corluy
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (291 download)
Download or read book Rates of Convergence in the Central Limit Theorem for Markov Chains written by Marc Corluy and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dieter Landers
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (31 download)
Download or read book On the Rate of Convergence in the Central Limit Theorem for Markov- Chains written by Dieter Landers and published by . This book was released on 1975 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hubert Hennion
Publisher : Springer
ISBN 13 : 3540446230
Total Pages : 150 pages
Book Rating : 4.5/5 (44 download)
Download or read book Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness written by Hubert Hennion and published by Springer. This book was released on 2003-07-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
Author : Peter Hall
Publisher :
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.F/5 ( download)
Download or read book Rates of Convergence in the Central Limit Theorem written by Peter Hall and published by . This book was released on 1982 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dmitry Dolgopyat
Publisher : Springer Nature
ISBN 13 : 3031326016
Total Pages : 348 pages
Book Rating : 4.0/5 (313 download)
Download or read book Local Limit Theorems for Inhomogeneous Markov Chains written by Dmitry Dolgopyat and published by Springer Nature. This book was released on 2023-07-31 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Author : Randal Douc
Publisher : Springer
ISBN 13 : 3319977040
Total Pages : 758 pages
Book Rating : 4.3/5 (199 download)
Download or read book Markov Chains written by Randal Douc and published by Springer. This book was released on 2018-12-11 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
Author : Yu.V. Prokhorov
Publisher : Springer Science & Business Media
ISBN 13 : 3662041723
Total Pages : 280 pages
Book Rating : 4.6/5 (62 download)
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
Author : P. Hall
Publisher : Academic Press
ISBN 13 : 1483263223
Total Pages : 321 pages
Book Rating : 4.4/5 (832 download)
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.
Author : WanSoo T. Rhee
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (655 download)
Download or read book Studies on the Rate of Convergence in the Central Limit Theorem written by WanSoo T. Rhee and published by . This book was released on 1979 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shlomo Levental
Publisher :
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.:/5 (89 download)
Download or read book Uniform Limit Theorems for Markov Chains written by Shlomo Levental and published by . This book was released on 1986 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Su Chen
Publisher : Stanford University
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.F/5 ( download)
Download or read book Consistency and Convergence Rate of Markov Chain Quasi Monte Carlo with Examples written by Su Chen and published by Stanford University. This book was released on 2011 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo methods have been widely used in various scientific disciplines for generation of samples from distributions that are difficult to simulate directly. The random numbers driving Markov Chain Monte Carlo algorithms are modeled as independent $\mathcal{U}[0,1)$ random variables. The class of distributions that could be simulated are largely broadened by using Markov Chain Monte Carlo. Quasi-Monte Carlo, on the other hand, aims to improve the accuracy of estimation of an integral over the multidimensional unit cube. By using more carefully balanced inputs, under some smoothness conditions the estimation error is converging at a higher rate than plain Monte Carlo. We would like to combine these two techniques, so that we can sample more accurately from a larger class of distributions. This method, called Markov Chain quasi-Monte Carlo (MCQMC), is the main topic of this work. We are going to replace the IID driving sequence used in MCMC algorithms by a deterministic sequence which is designed to be more uniform. Previously the justification for MCQMC is proved only for finite state space case. We are going to extend those results to some Markov Chains on continuous state spaces. We also explore the convergence rate of MCQMC under stronger assumptions. Lastly we present some numerical results for demonstration of MCQMC's performance. From these examples, the empirical benefits of more balanced sequences are significant.
Author : W.R. Gilks
Publisher : CRC Press
ISBN 13 : 1482214970
Total Pages : 505 pages
Book Rating : 4.4/5 (822 download)
Download or read book Markov Chain Monte Carlo in Practice written by W.R. Gilks and published by CRC Press. This book was released on 1995-12-01 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France,
Author : Oliver Jovanovski
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Convergence Rate Analysis of Markov Chains written by Oliver Jovanovski and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ravi R. Montenegro
Publisher : Now Publishers Inc
ISBN 13 : 1933019298
Total Pages : 133 pages
Book Rating : 4.9/5 (33 download)
Download or read book Mathematical Aspects of Mixing Times in Markov Chains written by Ravi R. Montenegro and published by Now Publishers Inc. This book was released on 2006 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Aspects of Mixing Times in Markov Chains is a comprehensive, well-written review of the subject that will be of interest to researchers and students in computer and mathematical sciences.
Author : George G. Yin
Publisher : Springer
ISBN 13 : 1461206278
Total Pages : 358 pages
Book Rating : 4.4/5 (612 download)
Download or read book Continuous-Time Markov Chains and Applications written by George G. Yin and published by Springer. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.
Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)
Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author :
Publisher : Univ of California Press
ISBN 13 : 0520367146
Total Pages : 774 pages
Book Rating : 4.5/5 (23 download)
Download or read book PROCEEDINGS OF THE SIXTH BERKELEY SYMPOSIUM ON MATHEMATICAL STATISTICS AND. written by and published by Univ of California Press. This book was released on 2021 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:
