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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 274–285
(Mi znsl6238)
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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
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.
Received: 21.10.2015
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
Linking options:
https://www.mathnet.ru/eng/znsl6238 https://www.mathnet.ru/eng/znsl/v441/p274
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Abstract page: | 144 | Full-text PDF : | 41 | References: | 36 |
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