Large Deviations For Markov Chains PDF Download
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Author | : Alejandro D. de Acosta |
Publisher | : |
Total Pages | : 264 |
Release | : 2022-10-12 |
Genre | : Mathematics |
ISBN | : 1009063359 |
Download Large Deviations for Markov Chains Book in PDF, ePub and Kindle
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 | : Alejandro D. de Acosta |
Publisher | : American Mathematical Soc. |
Total Pages | : 120 |
Release | : 2014-03-05 |
Genre | : Mathematics |
ISBN | : 0821890891 |
Download Large Deviations for Additive Functionals of Markov Chains Book in PDF, ePub and Kindle
Author | : Sibylle U. Nerz |
Publisher | : |
Total Pages | : 130 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Large Deviations for Markov Chains Book in PDF, ePub and Kindle
Author | : Jin Feng |
Publisher | : American Mathematical Soc. |
Total Pages | : 426 |
Release | : 2015-02-03 |
Genre | : Mathematics |
ISBN | : 1470418703 |
Download Large Deviations for Stochastic Processes Book in PDF, ePub and Kindle
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 | : Frank Hollander |
Publisher | : American Mathematical Soc. |
Total Pages | : 164 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821844359 |
Download Large Deviations Book in PDF, ePub and Kindle
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 | : Gilad Lerman |
Publisher | : |
Total Pages | : |
Release | : 1995 |
Genre | : Markov processes |
ISBN | : |
Download Large Deviations for Markov Chains Book in PDF, ePub and Kindle
Author | : S. R. S. Varadhan |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2016-12-08 |
Genre | : Mathematics |
ISBN | : 082184086X |
Download Large Deviations Book in PDF, ePub and Kindle
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 | : Firas Rassoul-Agha |
Publisher | : American Mathematical Soc. |
Total Pages | : 335 |
Release | : 2015-03-12 |
Genre | : Mathematics |
ISBN | : 0821875787 |
Download A Course on Large Deviations with an Introduction to Gibbs Measures Book in PDF, ePub and Kindle
This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the percolation approach. Beyond the large deviations of independent variables and Gibbs measures, later parts of the book treat large deviations of Markov chains, the Gärtner-Ellis theorem, and a large deviation theorem of Baxter and Jain that is then applied to a nonstationary process and a random walk in a dynamical random environment. The book has been used with students from mathematics, statistics, engineering, and the sciences and has been written for a broad audience with advanced technical training. Appendixes review basic material from analysis and probability theory and also prove some of the technical results used in the text.
Author | : S. R. S. Varadhan |
Publisher | : SIAM |
Total Pages | : 74 |
Release | : 1984-01-31 |
Genre | : Mathematics |
ISBN | : 0898711894 |
Download Large Deviations and Applications Book in PDF, ePub and Kindle
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Author | : A.D. Wentzell |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400918526 |
Download Limit Theorems on Large Deviations for Markov Stochastic Processes Book in PDF, ePub and Kindle
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.