Geodesic
On the spectral density of stationary processes and random fields
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 274-285 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2015_441_a16,
     author = {M. A. Lifshits and M. Peligrad},
     title = {On the spectral density of stationary processes and random fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {274--285},
     year = {2015},
     volume = {441},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a16/}
}
TY  - JOUR
AU  - M. A. Lifshits
AU  - M. Peligrad
TI  - On the spectral density of stationary processes and random fields
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 274
EP  - 285
VL  - 441
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a16/
LA  - en
ID  - ZNSL_2015_441_a16
ER  - 
%0 Journal Article
%A M. A. Lifshits
%A M. Peligrad
%T On the spectral density of stationary processes and random fields
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 274-285
%V 441
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a16/
%G en
%F ZNSL_2015_441_a16
M. A. Lifshits; M. Peligrad. On the spectral density of stationary processes and random fields. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 274-285. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a16/

[1] R. C. Bradley, “Basic properties of strong mixing conditions. A survey and some open questions”, Probab. Surv., 2 (2005), 107–144 | DOI | MR | Zbl

[2] R. C. Bradley, Introduction to Strong Mixing Conditions, v. 1–3, Kendrick Press, Heber City, UT, 2007

[3] P. J. Brockwell, R. A. Davis, Time Series: Theory and Methods, Springer, New York, 1991 | MR | Zbl

[4] A. V. Bulinski, A. N. Shyriaev, Theory of Random Processes, Fizmatlit, Moscow, 2003

[5] L. Carleson, “On convergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–157 | DOI | MR | Zbl

[6] S. R. S. Varadhan, Probability Theory, Courant Lecture Notes, 7, Amer. Math. Soc., 2001 | MR | Zbl

[7] D. Volný, Y. Wang, “An invariance principle for stationary random fields under Hannan's condition”, Stoch. Proc. Appl., 124 (2014), 4012–4029 | DOI | MR | Zbl