Stationary random fields in space and time with rational spectral densities

IEEE Transactions on Information Theory

Volumn 53, Issue 3, 2007, Pages 1019-1029

  Ma, Chunsheng ^a  

^a WICHITA STATE UNIVERSITY   (United States)

Author keywords

Correlation function; Fourier series; Fourier transform; Isotropic; Long range dependence; Power law decay; Spectral density; Stationary

Indexed keywords

CORRELATION THEORY; FOURIER SERIES; FOURIER TRANSFORMS; MATHEMATICAL MODELS; SPECTRAL DENSITY; TIME DOMAIN ANALYSIS;

POWER LAW DECAY; SPACE-TIME DOMAINS; SPATIAL NORMS; STATIONARY RANDOM FIELDS;

INFORMATION THEORY;

EID: 33947617795     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.890721     Document Type: Article

References (44)

1. H. Allouba and V. Goodman, "Market price of risk and random field driven models of term structure: A space-time change of measure look," in Finite and Infinite Dimensional Analysis in Honor of Leonard Gross (New Orleans, LA, 2001). Providence, RI: Amer. Math. Soc., 2003, pp. 37-44.
2. V. V. Anh, V. P. Knopova, and N. N. Leonenko, "Continuous-time stochastic processes with cyclical long-range dependence," Aust. N. Z. J. Stat., vol. 46, pp. 275-296, 2004.
3. O. E. Barndorff-Nielsen and N. N. Leonenko, "Spectral properties of superpositions of Ornstein-Uhlenbeck type processes," Methodol. Comput. Appl. Prob., vol. 7, pp. 335-352, 2005.
4. A. Brix and J. Møller, "Space-time multi-type log Gaussian Cox processes with a view to modeling weeds," Scand. J. Statist., vol. 28, pp. 471-488, 2001.
5. P. J. Brockwell, "A note on the embedding of discrete-time ARMA processes," J. Time Ser. Anal., vol. 16, pp. 451-460, 1995.
6. P. J. Brockwell, "Continuous-time ARMA processes," in Handbook of Statistics, D. N. Shanbhag and C. R. Rao, Eds. Amsterdam, The Netherlands: Elsevier Science B.V., 2001, vol. 19, pp. 249-276.
7. C. E. Buell, "Correlation functions for wind and geopotential on isobaric surfaces," J. Appl. Meteorology, vol. 11, pp. 51-59, 1972.
8. J.-P. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty. New York: Wiley, 1999.
9. G. Christakos, Modern Spatiotemporal Geostatistics. Oxford, U.K.: Oxford University Press, 2000.
10. N. Cressie, Statistics for Spatial Data, Revised ed. New York: Wiley, 1993.
11. N. Cressie and H. C. Huang, "Classes of nonseparable, spatio-temporal stationary covariance functions," J. Amer. Statist. Assoc., vol. 94, pp. 1330-1340, 1999.
12. T. Dalenius, J. Hájek, and S. Zubrzycki, "On plane sampling and related geometrical problems," in Proc. Fourth Berkeley Symp. Math. Statist. Prob., Berkeley, CA, 1961, vol. 1, pp. 125-150.
13. J. A. N. Filipe and M. M. Maule, "Effects of dispersal mechanisms on spatio-temporal development of epidemics," J. Theoret. Biol., vol. 226, pp. 125-141, 2004.
14. P. M. Fishman and D. L. Snyder, "The statistical analysis of space-time point processes," IEEE Trans. Inf. Theory, vol. IT-22, pp. 257-274, 1976.
15. G. Gaspri and S. E. Cohn, "Construction of correlation functions in two and three dimensions," Quart. J. Roy. Meteorol. Soc., vol. 125, pp. 723-757, 1999.
16. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic, 2000.
17. T. C. Haas, "Statistical assessment of spatio-temporal pollutant trends and meteorological transport models," Atmosph. Env., vol. 32, pp. 1865-1879, 1998.
18. J. Little, M. Goldstein, P. Jonathan, and K. den Heijer, "Spatio-temporal modeling of corrosion in an industrial furnance," Appl. Stoch. Models Bus. Ind., vol. 20, pp. 219-238, 2004.
19. C. Ma, "Long memory continuous-time correlation models," J. Appl. Prob., vol. 40, pp. 1133-1146, 2003.
20. C. Ma, "Spatial autoregression and related spatio-temporal models," J. Multivariate Anal., vol. 88, pp. 152-162, 2004.
21. C. Ma, "A class of stationary random fields with a simple correlation structure," J. Multivariate Anal., vol. 94, pp. 313-327, 2005.
22. C. Ma, "Linear combinations of space-time covariance functions and variograms," IEEE Trans. Signal Process., vol. 53, pp. 857-864, 2005.
23. C. Ma, "Spatio-temporal variograms and covariance models," Adv. Appl. Prob., vol. 37, pp. 706-725, 2005.
24. C. Ma, "Planar-temporal stationary correlation models that depend on the maximum norm," IEEE Trans. Signal Process., 2007, to be published.
25. G. Marion, G. Gibson, and E. Renshaw, "Estimating likelihoods for spatio-temporal models using importance sampling," Statist. Comput., vol. 13, pp. 111-119, 2003.
26. B. Matérn, Spatial Variation, 2nd ed. Berlin, Germany: Springer, 1986.
27. M. M. Meerschaert, D. A. Benson, H. P. Scheffler, and B. Baeumer, "Stochastic solution of space-time fractional diffusion equations," Phys. Rev. E, vol. 65, 2002.
28. Y. Mittal, "A class of isotropic covariance functions," Pacific J. Math., vol. 64, pp. 517-538, 1976.
29. D. E. Myers, S. De Iaco, D. Posa, and L. De Cesare, "Space-time radial basis functions," Comput. Math. Appl., vol. 43, pp. 539-549, 2002.
30. P. Northrop, "A clustered spatial-temporal model of rainfall," Proc. Roy. Soc. Lond. A, vol. 454, pp. 1875-1888, 1998.
31. D. S. Oliver, "Moving average for Gaussian simulation in two and three dimensions," Math. Geology, vol. 27, pp. 939-960, 1995.
32. S. Ørstavik, R. Carretero-González, and J. Stark, "Estimation of intensive quantities in spatio-temporal systems from time-series," Phys. D., vol. 147, pp. 204-220, 2000.
33. G. Peccati, "Explicit formulae for time-space Brownian chaos," Bernoulli, vol. 9, pp. 25-48, 2003.
34. I. J. Schoenberg, "Metric spaces and completely monotone functions," Ann. Math., vol. 39, pp. 811-841, 1938.
35. I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Canadian J. Phys., vol. 46, pp. 2133-2153, 1968.
36. M. L. Stein, "Sapce-time covariance functions," J. Amer. Statist. Assoc., vol. 100, pp. 310-321, 2005.
37. G. Storvik, A. Frigessi, and D. Hirst, "Stationary space-time Gaussian fields and their time autoregressive representation," Statist. Model., vol. 2, pp. 139-161, 2002.
38. T. von Kármán, "Progress in the statistical theory of turbulence," Proc. Nat. Acad. Sci. USA, vol. 34, pp. 530-539, 1948.
39. Z. Wang and G. B. Giannakis, "Outage mutual information of space-time MIMO channels," IEEE Trans. Inf. Theory, vol. 50, pp. 657-662, 2004.
40. H. S. Wheater, V. S. Isham, D. R. Cox, R. E. Chandler, A. Kakou, P. J. Northrop, L. Oh, C. Onof, and I. Rodriguez-Iturbe, "Spatial-temporal rainfall fields: Modeling and statistical aspects," Hydrol. Earth Sys. Sci., vol. 4, pp. 581-601, 2000.
41. P. Whittle, "On stationary processes in the plane," Biometrika, vol. 41, pp. 434-449, 1954.
42. C. K. Wikle, "A kernel-based spectral model for non-Gaussian spatio-temporal processes," Statist. Model., vol. 2, pp. 299-314, 2004.
43. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions. New York: Springer, 1987.
44. J. Zhuang, Y. Ogata, and D. Vere-Jones, "Stochastic declustering of space-time earthquake occurrences," J. Amer. Statist. Assoc., vol. 97, pp. 369-380, 2002.