On the rate of strong mixing in stationary Gaussian random fields

Raymond Cheng

Studia Mathematica (1992)

  • Volume: 101, Issue: 2, page 183-191
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Cheng, Raymond. "On the rate of strong mixing in stationary Gaussian random fields." Studia Mathematica 101.2 (1992): 183-191. <http://eudml.org/doc/215900>.

@article{Cheng1992,
abstract = {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.},
author = {Cheng, Raymond},
journal = {Studia Mathematica},
keywords = {stationary random field; strong mixing; prediction theory; spectral criteria; stationary Gaussian random field; strongly mixing},
language = {eng},
number = {2},
pages = {183-191},
title = {On the rate of strong mixing in stationary Gaussian random fields},
url = {http://eudml.org/doc/215900},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Cheng, Raymond
TI - On the rate of strong mixing in stationary Gaussian random fields
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 2
SP - 183
EP - 191
AB - 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.
LA - eng
KW - stationary random field; strong mixing; prediction theory; spectral criteria; stationary Gaussian random field; strongly mixing
UR - http://eudml.org/doc/215900
ER -

References

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  1. [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, New York 1976. Zbl0344.46071
  2. [2] R. Cheng, A strong mixing condition for second-order stationary random fields, this issue, 139-153. Zbl0809.60061
  3. [3] H. Helson and D. Sarason, Past and future, Math. Scand. 21 (1967), 5-16. 
  4. [4] I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes, Springer, New York 1978. 
  5. [5] S. V. Khrushchev and V. V. Peller, Hankel operators, best approximations, and stationary Gaussian processes, Russian Math. Surveys 37 (1982), 61-144. Zbl0505.60043
  6. [6] A. N. Kolmogorov and Yu. A. Rozanov, On a strong mixing condition for stationary Gaussian processes, Theory Probab. Appl. 5 (1960), 204-208. Zbl0106.12005
  7. [7] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 43-47. Zbl0070.13804
  8. [8] M. Rosenblatt, Stationary Sequences and Random Fields, Birkhäuser, Boston 1985. Zbl0597.62095
  9. [9] D. Sarason, An addendum to 'Past and Future', Math. Scand. 30 (1972), 62-64. Zbl0266.60023

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