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1991-1992 | 101 | 2 | 139-153
Tytuł artykułu

A strong mixing condition for second-order stationary random fields

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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(R_N) 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 $ℳ(R_N)$.
Czasopismo
Rocznik
Tom
101
Numer
2
Strony
139-153
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-04-02
poprawiono
1991-05-07
Twórcy
  • Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.
Bibliografia
  • [1] R. Cheng, The spectral measure of a regular stationary random field with the weak or strong commutation property, preprint.
  • [2] R. Cheng, Strong mixing in stationary fields, Ph.D. dissertation, University of Virginia, 1989.
  • [3] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York 1970.
  • [4] H. Dym and H. P. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem, Academic Press, New York 1976.
  • [5] U. Grenander and G. Szegö, Toeplitz Forms and Their Application, University of California Press, 1958.
  • [6] E. Hayashi, The spectral density of a strongly mixing stationary Gaussian process, Pacific J. Math. 96 (1981), 343-359.
  • [7] H. Helson and D. Lowdenslager, Prediction theory and Fourier series in several variables, I, Acta Math. 99 (1958), 165-202.
  • [8] H. Helson and D. Sarason, Past and future, Math. Scand. 21 (1967), 5-16.
  • [9] H. Helson and G. Szegö, A problem in prediction theory, Ann. Mat. Pura Appl. 51 (1960), 107-138.
  • [10] I. A. Ibragimov, On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition, Theory Probab. Appl. 10 (1965), 85-106; 15 (1970), 24-37.
  • [11] I. A. Ibragimov and V. N. Solev, A condition for the regularity of a Gaussian stationary process, Soviet Math. Dokl. 10 (1969), 371-375.
  • [12] G. Kallianpur, A. G. Miamee and H. Niemi, On the prediction theory of two-parameter stationary random fields, technical report No. 178, Center for Stochastic Processes, University of North Carolina, 1987.
  • [13] H. Korezlioglu et P. Loubaton, Prédiction des processus stationnaires au sense large sur Z² relativement aux demi-plans, C. R. Acad. Sci. Paris Sér. I 301 (1) (1985), 27-30.
  • [14] A. Makagon and H. Salehi, Stationary fields with positive angle, J. Multivariate Anal. 22 (1987), 106-125.
  • [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.
  • [16] T. Nakazi, The commutator of two projections in prediction theory, Bull. Austral. Math. Soc. 34 (1986), 65-71.
  • [17] T. Nakazi and K. Takahashi, Prediction n units of time ahead, Proc. Amer. Math. Soc. 80 (1980), 658-659.
  • [18] V. V. Peller and S. V. Khrushchev, Hankel operators, best approximations, and stationary Gaussian processes, Russian Math. Surveys 37 (1982), 61-144.
  • [19] Yu. A. Rozanov, On Gaussian fields with given conditional distributions, Theory Probab. Appl. 12 (1967), 381-391.
  • [20] D. Sarason, An addendum to 'Past and future', Math. Scand. 30 (1972), 62-64.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv101i2p139bwm
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