Large Deviations for Additive Functionals of Markov Chains.
de Acosta, Alejandro D.
Large Deviations for Additive Functionals of Markov Chains. - 1st ed. - 1 online resource (120 pages) - Memoirs of the American Mathematical Society ; v.228 . - Memoirs of the American Mathematical Society .
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 *( )> -- 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.
9781470414825
Large deviations.
Markov processes.
Additive functions.
Electronic books.
QA273.67 -- .A26 2013eb
519.233
Large Deviations for Additive Functionals of Markov Chains. - 1st ed. - 1 online resource (120 pages) - Memoirs of the American Mathematical Society ; v.228 . - Memoirs of the American Mathematical Society .
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 *( )> -- 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.
9781470414825
Large deviations.
Markov processes.
Additive functions.
Electronic books.
QA273.67 -- .A26 2013eb
519.233