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Teoriya Veroyatnostei i ee Primeneniya, 1997, Volume 42, Issue 1, Pages 35–50
DOI: https://doi.org/10.4213/tvp1710 (Mi tvp1710) 		 
This article is cited in 33 scientific papers (total in 33 papers)

Effective convergence in probability and an ergodic theorem for individual random sequences

V. V. V'yugin

Institute for Information Transmission Problems, Russian Academy of Sciences
Full-text PDF (950 kB) Citations (33)
DOI: https://doi.org/10.4213/tvp1710
Abstract: An algorithmic analysis of the ergodic theorem for a measure-preserving transformation is given. We prove that the classical ergodic theorem is not algorithmically effective. We present a formulation and a proof of the ergodic theorem for individual random sequences based on A. N. Kolmogorov's algorithmic approach to the substantiation of the theory of probability and information theory.
Keywords: ergodic theorem, quasiergodic theorem, stationary measure, convergence in probability, convergence almost everywhere, algorithm, random sequence, algorithmical randomness.
Received: 12.07.1996
English version:
Theory of Probability and its Applications, 1998, Volume 42, Issue 1, Pages 39–50
DOI: https://doi.org/10.1137/S0040585X97975915
Bibliographic databases:
Language: Russian
Citation: V. V. V'yugin, “Effective convergence in probability and an ergodic theorem for individual random sequences”, Teor. Veroyatnost. i Primenen., 42:1 (1997), 35–50; Theory Probab. Appl., 42:1 (1998), 39–50
Citation in format AMSBIB
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\paper Effective convergence in probability and an ergodic theorem for individual random sequences
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\pages 35--50
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\zmath{https://zbmath.org/?q=an:0917.60039}
\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 1
\pages 39--50
\crossref{https://doi.org/10.1137/S0040585X97975915}
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Linking options:
  • https://www.mathnet.ru/eng/tvp1710
  • https://doi.org/10.4213/tvp1710
  • https://www.mathnet.ru/eng/tvp/v42/i1/p35
    • This publication is cited in the following 33 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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