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Author : Zachariah Espe Dietz
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (539 download)
Download or read book Large Deviations of a Class of Non-homogeneous Markov Chains written by Zachariah Espe Dietz and published by . This book was released on 2003 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Enzo Olivieri
Publisher : Cambridge University Press
ISBN 13 : 9780521591638
Total Pages : 540 pages
Book Rating : 4.5/5 (916 download)
Download or read book Large Deviations and Metastability written by Enzo Olivieri and published by Cambridge University Press. This book was released on 2005-02-21 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
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 : Alejandro D. de Acosta
Publisher :
ISBN 13 : 9781470414825
Total Pages : 120 pages
Book Rating : 4.4/5 (148 download)
Download or read book Large Deviations for Additive Functionals of Markov Chains written by Alejandro D. de Acosta and published by . This book was released on 2014-10-03 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a Markov chain {X?} with general state space S and f: S?R ?, the large deviation principle for {n ?1 ? =1 f(X?)} is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f, for a broad class of initial distributions. This result is extended to the case when f takes values in a separable Banach space. Assuming only geometric ergodicity and under a non-degeneracy condition, a local large deviation result is proved for bounded f. A central analytical tool is the transform kernel, whose required properties, including new results, are established. The rate function in the large deviation results is expressed in terms of the convergence parameter of the transform kernel.
Author : S. R. S. Varadhan
Publisher : American Mathematical Soc.
ISBN 13 : 082184086X
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)
Download or read book Large Deviations written by S. R. S. Varadhan and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Author : Mikhail Menshikov
Publisher : Cambridge University Press
ISBN 13 : 1316867366
Total Pages : 385 pages
Book Rating : 4.3/5 (168 download)
Download or read book Non-homogeneous Random Walks written by Mikhail Menshikov and published by Cambridge University Press. This book was released on 2016-12-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Author : Alejandro D. de Acosta
Publisher :
ISBN 13 : 1009063359
Total Pages : 264 pages
Book Rating : 4.0/5 (9 download)
Download or read book Large Deviations for Markov Chains written by Alejandro D. de Acosta and published by . This book was released on 2022-10-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Author : V. M. Blinovskii
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4.E/5 ( download)
Download or read book Process Level Large Deviations for a Class of Piece-wise Homogeneous Random Walks written by V. M. Blinovskii and published by . This book was released on 1993 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.D. Wentzell
Publisher : Springer
ISBN 13 : 9789401073257
Total Pages : 176 pages
Book Rating : 4.0/5 (732 download)
Download or read book Limit Theorems on Large Deviations for Markov Stochastic Processes written by A.D. Wentzell and published by Springer. This book was released on 2012-08-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et BIOi. .... si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities 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.
Author : Yu. M. Suhov
Publisher : Cambridge University Press
ISBN 13 : 0521847672
Total Pages : 499 pages
Book Rating : 4.5/5 (218 download)
Download or read book Probability and Statistics by Example: Volume 2, Markov Chains: A Primer in Random Processes and Their Applications written by Yu. M. Suhov and published by Cambridge University Press. This book was released on 2008-04-24 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject is critical in many modern applications such as mathematical finance, quantitative management, insurance and actuarial studies.
Author : Harry Cohn
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (219 download)
Download or read book On a Class of Non-homogeneous Markov Chains written by Harry Cohn and published by . This book was released on 1981 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anton Bovier
Publisher :
ISBN 13 :
Total Pages : 55 pages
Book Rating : 4.:/5 (678 download)
Download or read book Sample Path Large Deviations for a Class of Markov Chains Related to Disordered Mean Field Models written by Anton Bovier and published by . This book was released on 1999 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank Hollander
Publisher : American Mathematical Soc.
ISBN 13 : 9780821844359
Total Pages : 164 pages
Book Rating : 4.8/5 (443 download)
Download or read book Large Deviations written by Frank Hollander and published by American Mathematical Soc.. This book was released on 2000 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Author :
Publisher :
ISBN 13 :
Total Pages : 574 pages
Book Rating : 4.3/5 (91 download)
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jin Feng
Publisher : American Mathematical Soc.
ISBN 13 : 1470418703
Total Pages : 426 pages
Book Rating : 4.4/5 (74 download)
Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2015-02-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Author :
Publisher :
ISBN 13 :
Total Pages : 806 pages
Book Rating : 4.3/5 (91 download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mufa Chen
Publisher : World Scientific
ISBN 13 : 9812388117
Total Pages : 610 pages
Book Rating : 4.8/5 (123 download)
Download or read book From Markov Chains to Non-equilibrium Particle Systems written by Mufa Chen and published by World Scientific. This book was released on 2004 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.
