On the rate of strong mixing in stationary Gaussian random fields

• Autorzy: Raymond Cheng
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

stationary random field; strong mixing; prediction theory

Kategorie tematyczne

• 60G25: Prediction theory
• 60G60: Random fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 2
• Strony: 183-191

Daty

wydano

1992

otrzymano

1990-11-08

Twórcy

autor

Raymond Cheng

• Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.

Bibliografia

• [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, New York 1976.
• [2] R. Cheng, A strong mixing condition for second-order stationary random fields, this issue, 139-153.
• [3] H. Helson and D. Sarason, Past and future, Math. Scand. 21 (1967), 5-16.
• [4] I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes, Springer, New York 1978.
• [5] S. V. Khrushchev and V. V. Peller, Hankel operators, best approximations, and stationary Gaussian processes, Russian Math. Surveys 37 (1982), 61-144.
• [6] A. N. Kolmogorov and Yu. A. Rozanov, On a strong mixing condition for stationary Gaussian processes, Theory Probab. Appl. 5 (1960), 204-208.
• [7] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 43-47.
• [8] M. Rosenblatt, Stationary Sequences and Random Fields, Birkhäuser, Boston 1985.
• [9] D. Sarason, An addendum to 'Past and Future', Math. Scand. 30 (1972), 62-64.