The L2 structure of harmonizable random fields
Resumo
In this paper, we study a large class of harmonizable random fields (r:f: for short) when the indexing set is Zd, d> 2. This class of processes is a generalization of wide sense stationary r:f: have been investigated in several varieties of subjects and constitute an important class of nonstationary r:f:. So, conditions necessary and suffcient ensuring the stability of the linear transformation of particular class are given.
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Referências
S. Cambanis, B. Liu, On harmonizable stochastic processes. Information and control, 17, 183-202, (1970).
D.K. Chang, M.M. Rao, Bimeasures and nonstationary processes, Real and stochastic analysis (ed. M.M. Rao), Wiley, New York, (1987).
H. Cramer, A Contribution to the Theory of Stochastic Processes, Proc. Second Berkeley Symp. Math. Statist. Prob., 2, 55-77, (1952).
N. Cressie, Statistics for Spatial Data, rev. ed. New York: Wiley,(1993).
R. Dahlhaus, Locally stationary processes. Handbook of Statistics, Time Series Analysis: Methods and Applications, 351-408, (2012).
D. Dehay, R. Moche, Strongly harmonizing operators and strongly harmonizable approximations of continuous random fields on LCA groups. Stochastic processes and their applications, 29(1), 129-139, (1988).
C. Gaetan, X. Guyon, Spatial Statistics and Modeling. New York: Springer, (2010).
K. Kimouche, A. Bibi,The generalizations of the multidimensional Fourier transform. Book Chapter, (2023). doi: 10.5281/zenodo.10416976
N. Leonenko, Limit Theorems for Random Fields with Singular. Spectrum, Springer. (1999).
H. Mehlman, Marc, Prediction and fundamental moving averages for discrete multidimensional harmonizable processes. Journal of Multivariate Analysis, 147-170. (1992).
A. Miamee, Periodically Correlated Processes and Their Stationary Dilations. SIAM., J. Appl. Math. 50, 1194-1199, (1990).
M.M. Rao, Harmonizable, Cram´er and Karhunen classes of processes , in Handbook of Statistics, E. J. Hannan, P. R. Krishnaiah, and M. M. Rao, Eds, 5, ch. 10, 279-310, (1985).
M.M. Rao,Harmonizable Processes: Structure Theory, L’Enseign Math., 28, 295-351, (1984).
M.M. Rao, Real and stochastic analysis : current trends. World Scientific Publishing Co. Pte. Ltd.(2014).
M.M. Rao, Characterizations of harmonizable fields. Nonlinear Analysis 63, pp. 935 - 947, (2005).
M. M. Rao, The spectral domain of multivariate harmonizable processes, Proc. Nat. Acad. Sci. (U.S.A.) 81, 4611-4612, (1984).
M. M. Rao, Stochastic processes : harmonizable theory . World Scientific Publishing Co. Pte. Ltd., (2021).
R. J. Swift, The structure of harmonizable isotropic random fields. Stochastic Analysis and Applications, 12(5), 583-616.(1994).
R. J. Swift, Harmonizable locally spatially isotropic random fields. Revista Colombiana de Matem aticas, 33(2), 91-103, (1999).
P. Whittle, On stationary processes in the plane, Biometrika, 41, 434-449, (1954).
A. M. Yaglom, Correlation theory of stationary and related random functions, Vol. II. New York: Springer, (1987).
A. M. Yadrenko, Spectral theory of random fields, Optimization Software, New York, (1983).
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