de Acosta Large Deviations for Markov Chains

Erscheinungsjahr 2022
ISBN: 978-1-009-06335-7
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 229

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

de Acosta, Alejandro D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Preface; 1. Introduction; 2. Lower bounds and a property of lambda; 3. Upper bounds I; 4. Identification and reconciliation of rate functions; 5. Necessary conditions – bounds on the rate function, invariant measures, irreducibility and recurrence; 6. Upper bounds II – equivalent analytic conditions; 7. Upper bounds III – sufficient conditions; 8. The large deviations principle for empirical measures; 9. The case when S is countable and P is matrix irreducible; 10. Examples; 11. Large deviations for vector-valued additive functionals; Appendix A; Appendix B; Appendix C; Appendix D; Appendix E; Appendix F; Appendix G; Appendix H; Appendix I; Appendix J; Appendix K; References; Author index; Subject index.

Über Autor(innen)

de Acosta, Alejandro D.
Alejandro D. de Acosta is Professor Emeritus in the Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University. He has taught at the University of California at Berkeley, Massachusetts Institute of Technology, Universidad Nacional de La Plata and Universidad Nacional de Buenos Aires (Argentina), Instituto Venezolano de Investigaciones Científicas, University of Wisconsin–Madison, and, since 1983, at Case Western Reserve University. He is a Fellow of the Institute of Mathematical Statistics, and has served on the editorial boards of the Annals of Probability and the Journal of Theoretical Probability. He has published research papers in a number of areas of Probability Theory.