Large Deviations for Additive Functionals of Markov Chains.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. The transform kernels _{ } and their convergence parameters -- 2.1. Irreducibility -- 2.2. Small functions and measures -- 2.3. The convergence parameter -- 2.4. The period of _{ } and aperiodicity -- Chapter 3. Comparison of Λ( ) and _{ }( ) -- Chapter 4. Proof of Theorem 1 -- Chapter 5. A characteristic equation and the analyticity of Λ_{ }: the case when has an atom ∈ ⁺ satisfying *( )&gt -- 0 -- Chapter 6. Characteristic equations and the analyticity of Λ_{ }: the general case when is geometrically ergodic -- Chapter 7. Differentiation formulas for _{ } and Λ_{ } in the general case and their consequences -- Chapter 8. Proof of Theorem 2 -- Chapter 9. Proof of Theorem 3 -- Chapter 10. Examples -- Chapter 11. Applications to an autoregressive process and to reflected random walk -- 11.1. Application of Theorem 1 to an autoregressive process -- 11.2. Application of Theorem 2 to reflected random walk -- Appendix -- AI. Renewal sequences -- AII. Complex kernels and their associated renewal sequences -- AIII. Renewal characterization of the convergence parameter -- AIV. Some consequences of ergodicity -- AV. Geometric ergodicity -- Background comments -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.