Large Deviations for Additive Functionals of Markov Chains (Memoirs of the American Mathematical Society)

Large Deviations for Additive Functionals of Markov Chains (Memoirs of the American Mathematical Society)

By: Peter Ney (author), Alejandro De Acosta (author)Paperback

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Description

For a Markov chain {X?} with general state space S and f:S?R ?, the large deviation principle for {n ?1 ? ??=1 f(X?)} is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f , for a broad class of initial distributions. This result is extended to the case when f takes values in a separable Banach space. Assuming only geometric ergodicity and under a non-degeneracy condition, a local large deviation result is proved for bounded f. A central analytical tool is the transform kernel, whose required properties, including new results, are established. The rate function in the large deviation results is expressed in terms of the convergence parameter of the transform kernel.

About Author

Alejandro D. de Acosta is a Professor Emeritus of Mathematics.

Contents

IntroductionThe transform kernels Kg and their convergence parametersComparison of ?(g) and ? ? (g)Proof of Theorem 1A characteristic equation and the analyticity of ? f : the case when P has an atom C?S satisfying ? (C)> 0Characteristic equations and the analyticity of ? f: the general case when P is geometrically ergodicDifferentiation formulas for u g and ? f in the general case and their consequencesProof of Theorem 2Proof of Theorem 3ExamplesApplications to an autoregressive process and to reflected random walkAppendixBackground commentsReferences

Product Details

  • ISBN13: 9780821890899
  • Format: Paperback
  • Number Of Pages: 108
  • ID: 9780821890899
  • ISBN10: 0821890891

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