Rosenblatt showed that a stationary Gaussian random field is strongly mixing if it has a positive, continuous spectral density. In this article, spectral criteria are given for the rate of strong mixing in such a field.
@article{bwmeta1.element.bwnjournal-article-smv101i2p183bwm, author = {Raymond Cheng}, title = {On the rate of strong mixing in stationary Gaussian random fields}, journal = {Studia Mathematica}, volume = {103}, year = {1992}, pages = {183-191}, zbl = {0809.60062}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p183bwm} }
Cheng, Raymond. On the rate of strong mixing in stationary Gaussian random fields. Studia Mathematica, Tome 103 (1992) pp. 183-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p183bwm/
[00000] [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, New York 1976. | Zbl 0344.46071
[00001] [2] R. Cheng, A strong mixing condition for second-order stationary random fields, this issue, 139-153. | Zbl 0809.60061
[00002] [3] H. Helson and D. Sarason, Past and future, Math. Scand. 21 (1967), 5-16.
[00003] [4] I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes, Springer, New York 1978.
[00004] [5] S. V. Khrushchev and V. V. Peller, Hankel operators, best approximations, and stationary Gaussian processes, Russian Math. Surveys 37 (1982), 61-144. | Zbl 0505.60043
[00005] [6] A. N. Kolmogorov and Yu. A. Rozanov, On a strong mixing condition for stationary Gaussian processes, Theory Probab. Appl. 5 (1960), 204-208. | Zbl 0106.12005
[00006] [7] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 43-47. | Zbl 0070.13804
[00007] [8] M. Rosenblatt, Stationary Sequences and Random Fields, Birkhäuser, Boston 1985. | Zbl 0597.62095
[00008] [9] D. Sarason, An addendum to 'Past and Future', Math. Scand. 30 (1972), 62-64. | Zbl 0266.60023