Markov Chains

Part I Foundations.- Markov Chains: Basic Definitions.- Examples of Markov Chains.- Stopping Times and the Strong Markov Property.- Martingales, Harmonic Functions and Polsson-Dirichlet Problems.- Ergodic Theory for Markov Chains.- Part II Irreducible Chains: Basics.- Atomic Chains.- Markov Chains on a Discrete State Space.- Convergence of Atomic Markov Chains.- Small Sets, Irreducibility and Aperiodicity.- Transience, Recurrence and Harris Recurrence.- Splitting Construction and Invariant Measures.- Feller and T-kernels.- Part III Irreducible Chains: Advanced Topics.- Rates of Convergence for Atomic Markov Chains.- Geometric Recurrence and Regularity.- Geometric Rates of Convergence.- (f, r)-recurrence and Regularity.- Subgeometric Rates of Convergence.- Uniform and V-geometric Ergodicity by Operator Methods.- Coupling for Irreducible Kernels.- Part IV Selected Topics.- Convergence in the Wasserstein Distance.- Central Limit Theorems.- Spectral Theory.- Concentration Inequalities.- Appendices.- A Notations.- B Topology, Measure, and Probability.- C Weak Convergence.- D Total and V-total Variation Distances.- E Martingales.- F Mixing Coefficients.- G Solutions to Selected Exercises.

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• Probabilidade e Estatística
• Estocástica

Markov Chains;Geometric Ergodicity;Ergodic Theory;Markov Property;Potential Theory;Operator Theory;Limit Theorems;Martingales