A strong mixing condition for second-order stationary random fields

Raymond Cheng

Studia Mathematica (1992)

  • Volume: 101, Issue: 2, page 139-153
  • ISSN: 0039-3223

Abstract

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Let X m n be a second-order stationary random field on Z². Let ℳ(L) be the linear span of X m n : m ≤ 0 , n ∈ Z , and ℳ(RN) the linear span of X m n : m ≥ N , n ∈ Z . Spectral criteria are given for the condition l i m N → ∞ c N = 0 , where c N is the cosine of the angle between ℳ(L) and ℳ ( R N ) .

How to cite

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Cheng, Raymond. "A strong mixing condition for second-order stationary random fields." Studia Mathematica 101.2 (1992): 139-153. <http://eudml.org/doc/215897>.

@article{Cheng1992,
abstract = {Let $\{X_\{mn\}\}$ be a second-order stationary random field on Z². Let ℳ(L) be the linear span of $\{X_\{mn\}: m ≤ 0, n ∈ Z\}$, and ℳ(RN) the linear span of $\{X_\{mn\}: m ≥ N, n ∈ Z\}$. Spectral criteria are given for the condition $lim_\{N→∞\} c_N = 0$, where $c_N$ is the cosine of the angle between ℳ(L) and $ℳ(R_N)$.},
author = {Cheng, Raymond},
journal = {Studia Mathematica},
keywords = {stationary random field; prediction theory; strong mixing; spectral criteria},
language = {eng},
number = {2},
pages = {139-153},
title = {A strong mixing condition for second-order stationary random fields},
url = {http://eudml.org/doc/215897},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Cheng, Raymond
TI - A strong mixing condition for second-order stationary random fields
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 2
SP - 139
EP - 153
AB - Let ${X_{mn}}$ be a second-order stationary random field on Z². Let ℳ(L) be the linear span of ${X_{mn}: m ≤ 0, n ∈ Z}$, and ℳ(RN) the linear span of ${X_{mn}: m ≥ N, n ∈ Z}$. Spectral criteria are given for the condition $lim_{N→∞} c_N = 0$, where $c_N$ is the cosine of the angle between ℳ(L) and $ℳ(R_N)$.
LA - eng
KW - stationary random field; prediction theory; strong mixing; spectral criteria
UR - http://eudml.org/doc/215897
ER -

References

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  2. [2] R. Cheng, Strong mixing in stationary fields, Ph.D. dissertation, University of Virginia, 1989. 
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  14. [14] A. Makagon and H. Salehi, Stationary fields with positive angle, J. Multivariate Anal. 22 (1987), 106-125. Zbl0622.60051
  15. [15] A. G. Miamee and H. Niemi, On the angle for stationary random fields, technical report No. 92, Department of Statistics, University of North Carolina at Chapel Hill, 1985. Zbl0805.60046
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  20. [20] D. Sarason, An addendum to 'Past and future', Math. Scand. 30 (1972), 62-64. Zbl0266.60023

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