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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 364, Pages 88–108 (Mi znsl3152)  

This article is cited in 17 scientific papers (total in 17 papers)

Martingale-coboundary representation for a class of stationary random fields

M. I. Gordin

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
References:
Abstract: It is known that under some conditions a stationary random sequence admits a representation as the sum of two others: one of them is a martingale difference sequence and another is a so-called coboundary. Such a representation can be used for proving some limit theorems by means of the martingale approximation.
A multi-dimensional version of such a decomposition is presented in the paper for a class of random fields generated by several commuting non-invertible probability preserving transformations. In this representation summands of mixed type appear which behave with respect to some group of directions of the parameter space as reversed multiparameter martingale differences (in the sense of one of several known definitions) while they look as coboundaries relative to the other directions. Applications to limit theorems will be published elsewhere. Bibl. – 14 titles.
Received: 16.06.2008
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 163, Issue 4, Pages 363–374
DOI: https://doi.org/10.1007/s10958-009-9679-5
Bibliographic databases:
UDC: 512.2
Language: Russian
Citation: M. I. Gordin, “Martingale-coboundary representation for a class of stationary random fields”, Probability and statistics. Part 14–2, Zap. Nauchn. Sem. POMI, 364, POMI, St. Petersburg, 2009, 88–108; J. Math. Sci. (N. Y.), 163:4 (2010), 363–374
Citation in format AMSBIB
\Bibitem{Gor09}
\by M.~I.~Gordin
\paper Martingale-coboundary representation for a~class of stationary random fields
\inbook Probability and statistics. Part~14--2
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 364
\pages 88--108
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3152}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 163
\issue 4
\pages 363--374
\crossref{https://doi.org/10.1007/s10958-009-9679-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70549106455}
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  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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