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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 274–285 (Mi znsl6238)  
This article is cited in 3 scientific papers (total in 3 papers)

On the spectral density of stationary processes and random fields

M. A. Lifshitsab, M. Peligradc

a MAI, Linköping University, Sweden
b Department of Mathematics and Mechanics, St. Petersburg State University, Stary Peterhof, 198504, Russia
c Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, Oh 45221-0025, USA
Full-text PDF (177 kB) Citations (3)
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Abstract: In this note we show that a stationary sequence obtained by applying a fixed deterministic function to the shifts of a stationary sequence (satisfying a mild regularity condition) has a spectral density. In the multiparametric setting, we obtain a similar result for a function of a shifted i.i.d. field.
Key words and phrases: stationary processes, stationary random fields, spectral density.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00172
Saint Petersburg State University 6.38.672.2013
Charles Phelps Taft Research Center
National Science Foundation DMS-1512936
Supported by grants RFBR 13-01-00172, SPbSU 6.38.672.2013; Partially supported by a Taft research center grant and NSF grant DMS-1512936.
Received: 21.10.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 5, Pages 789–797
DOI: https://doi.org/10.1007/s10958-016-3147-9
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: English
Citation: M. A. Lifshits, M. Peligrad, “On the spectral density of stationary processes and random fields”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 274–285; J. Math. Sci. (N. Y.), 219:5 (2016), 789–797
Citation in format AMSBIB
\Bibitem{LifPel15}
\by M.~A.~Lifshits, M.~Peligrad
\paper On the spectral density of stationary processes and random fields
\inbook Probability and statistics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 441
\pages 274--285
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6238}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3504510}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 5
\pages 789--797
\crossref{https://doi.org/10.1007/s10958-016-3147-9}
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    • 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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