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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 11, Fasc. 2,
pages 157 - 167
 

ON SPECTRAL DENSITY ESTIMATES FOR A GAUSSIAN PERIODICALLY CORRELATED RANDOM FIELD

V. G. Alekseev

Abstract: We consider a random field q(t), t = (t ,t ) (- R2, 1 2 having mean value zero and the correlation function B(t,t) = B(t ,t ,t,t ) = Eq(t + t ,t + t)q(t,t ), 1 2 1 2 1 1 2 2 1 2 which is periodic in the sense that B(t + T ,t + T ,t) =_ B(t + T,t ,t) =_ B(t ,t,t) 1 1 2 2 1 1 2 1 2 (here the periods T 1 and T 2 are positive). It is shown that under broad conditions the spectral decomposition of the correlation function B(t,t) is represented by the countable set of spectral densities f (c ,c ) j1j2 1 2 where (j,j ) (- Z2 1 2 and (c ,c ) (- R2. 1 2 For the case where the random field under consideration is Gaussian, nonparametric estimates of the spectral densities f (c ,c ) j1j2 1 2 are introduced and studied.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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