Large Deviations for Additive Functionals of Markov Chains
Author: Alejandro D. de Acosta
Publisher: American Mathematical Soc.
Published: 2014-03-05
Total Pages: 120
ISBN-13: 0821890891
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Large Deviations for Additive Functionals of Markov Exhangeable Sequences
Author: Grant Izmirlian
Publisher:
Published: 1993
Total Pages: 194
ISBN-13:
DOWNLOAD EBOOKLarge Deviations for Markov Chains
Author: Alejandro D. de Acosta
Publisher:
Published: 2022-10-12
Total Pages: 264
ISBN-13: 1009063359
DOWNLOAD EBOOKThis 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.
Large Deviations Techniques and Applications
Author: Amir Dembo
Publisher: Springer Science & Business Media
Published: 2009-11-03
Total Pages: 409
ISBN-13: 3642033113
DOWNLOAD EBOOKLarge deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.
Large Deviations
Author: Jean-Dominique Deuschel
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 298
ISBN-13: 082182757X
DOWNLOAD EBOOKThis is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
Some Limit Theorems in Statistics
Author: R. R. Bahadur
Publisher: SIAM
Published: 1971-01-31
Total Pages: 48
ISBN-13: 0898711754
DOWNLOAD EBOOKA discussion of topics in the theory of large deviations and of aspects of estimation and testing in large samples.
Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach
Author: Jochen Denzler
Publisher: American Mathematical Soc.
Published: 2015-02-06
Total Pages: 94
ISBN-13: 1470414082
DOWNLOAD EBOOKThis paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.
Analysis of the Hodge Laplacian on the Heisenberg Group
Author: Detlef Muller
Publisher: American Mathematical Soc.
Published: 2014-12-20
Total Pages: 104
ISBN-13: 1470409399
DOWNLOAD EBOOKThe authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
Local Limit Theorems for Inhomogeneous Markov Chains
Author: Dmitry Dolgopyat
Publisher: Springer Nature
Published: 2023-07-31
Total Pages: 348
ISBN-13: 3031326016
DOWNLOAD EBOOKThis 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.
A Weak Convergence Approach to the Theory of Large Deviations
Author: Paul Dupuis
Publisher: John Wiley & Sons
Published: 1997-02-27
Total Pages: 522
ISBN-13: 9780471076728
DOWNLOAD EBOOKApplies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
