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Limit Theorems for Functionals of Ergodic Markov Chains with General State Space.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1999Copyright date: ©1999Edition: 1st edDescription: 1 online resource (225 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470402532
Subject(s): Genre/Form: Additional physical formats: Print version:: Limit Theorems for Functionals of Ergodic Markov Chains with General State SpaceDDC classification:
  • 510 s;519.2
LOC classification:
  • QA274.7 -- .C44 1999eb
Online resources:
Contents:
Intro -- Contents -- Introduction -- Chapter I. Split Chain and Regeneration -- I-1 Motivation and notation -- I-2 Split chain -- I-3 Maximal and minimal inequalities -- I-4 Maximal integrability on small sets -- Chapter II. The Central Limit Theorem -- II-1 Introduction -- II-2 Validity of CLT -- II-3 Identification of the limiting variance in the CLT -- II-4 The CLT and the ergodicity conditions -- Chapter III. The Law of the Iterated Logarithm -- III-1 Introduction -- III-2 The LIL and CLT -- III-3 Some remarks on the limit set -- III-4 The LIL in vector setting -- III-5 Some consequences -- III-6 Supplement -- Chapter IV. The moderate Deviation Principle -- IV-1 Introduction -- IV-2 Upper bounds -- IV-3 Lower bounds - for chains with a small set of order 1 -- IV-4 Lower bounds „ when ξ is bounded -- IV-5 Lower bounds „ when ξ ∈ CLT -- Appendix -- References.
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Intro -- Contents -- Introduction -- Chapter I. Split Chain and Regeneration -- I-1 Motivation and notation -- I-2 Split chain -- I-3 Maximal and minimal inequalities -- I-4 Maximal integrability on small sets -- Chapter II. The Central Limit Theorem -- II-1 Introduction -- II-2 Validity of CLT -- II-3 Identification of the limiting variance in the CLT -- II-4 The CLT and the ergodicity conditions -- Chapter III. The Law of the Iterated Logarithm -- III-1 Introduction -- III-2 The LIL and CLT -- III-3 Some remarks on the limit set -- III-4 The LIL in vector setting -- III-5 Some consequences -- III-6 Supplement -- Chapter IV. The moderate Deviation Principle -- IV-1 Introduction -- IV-2 Upper bounds -- IV-3 Lower bounds - for chains with a small set of order 1 -- IV-4 Lower bounds „ when ξ is bounded -- IV-5 Lower bounds „ when ξ ∈ CLT -- Appendix -- 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.

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