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Sbornik: Mathematics, 2009, Volume 200, Issue 5, Pages 683–696
DOI: https://doi.org/10.1070/SM2009v200n05ABEH004015 (Mi sm7486) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Martingale ergodic and ergodic martingale processes with continuous time

I. V. Podvigin

Novosibirsk State University
English version PDF (296 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2009v200n05ABEH004015
Abstract: In a paper dedicated to unifying martingales and ergodic averages, Kachurovskiǐ introduced certain unifying discrete-time martingale ergodic and ergodic martingale processes, for which he proved convergence theorems and established maximal and dominant inequalities. Our purpose in this article is to obtain similar results for such processes with continuous time. In addition, the results are used to assert convergence of yet another unifying process relating to Rota's approach to unification of martingales and Abel ergodic averages.
Bibliography: 13 titles.
Keywords: ergodic averages, regular martingale, positive $\mathrm{L_1}{-}\mathrm{L_\infty}$-contraction.
Received: 13.11.2008 and 01.12.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 5, Pages 55–70
DOI: https://doi.org/10.4213/sm7486
Bibliographic databases:
UDC: 517.987+519.216
MSC: 60G44
Language: English
Original paper language: Russian
Citation: I. V. Podvigin, “Martingale ergodic and ergodic martingale processes with continuous time”, Mat. Sb., 200:5 (2009), 55–70; Sb. Math., 200:5 (2009), 683–696
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v200/i5/p55
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:827
    Russian version PDF:310
    English version PDF:16
    References:78
    First page:14
     
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