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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 172–200 (Mi tm461)  
This article is cited in 8 scientific papers (total in 8 papers)

General Theories Unifying Ergodic Averages and Martingales

A. G. Kachurovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (349 kB) Citations (8)
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Abstract: The curious fact that the behavior of ergodic averages is analogous to the behavior of (reversed) martingales has long been known. For the last 60 years, at least five different approaches have been proposed to the construction of a unifying theory: by M. Jerison (1955), G. C. Rota (1961), A. and C. Ionescu Tulcea (1963), A.M. Vershik (1960s), and A.G. Kachurovskii (1998). The aim of the present survey is to carry out a comparative analysis of all the approaches, with special focus being placed on the fifth approach, which is due to the present author and has not yet been published in full detail. Moreover, the comparative analysis carried out in the survey has led to a new, the sixth, approach.
Received in June 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 160–187
DOI: https://doi.org/10.1134/S0081543807010099
Bibliographic databases:
UDC: 517.987+519.216
Language: Russian
Citation: A. G. Kachurovskii, “General Theories Unifying Ergodic Averages and Martingales”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 172–200; Proc. Steklov Inst. Math., 256 (2007), 160–187
Citation in format AMSBIB
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\by A.~G.~Kachurovskii
\paper General Theories Unifying Ergodic Averages and Martingales
\inbook Dynamical systems and optimization
\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 256
\pages 172--200
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm461}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336899}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 160--187
\crossref{https://doi.org/10.1134/S0081543807010099}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248366939}
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    • This publication is cited in the following 8 articles:
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