Geodesic
On estimation in random fields generated by linear stochastic partial differential equations
Mathematica slovaca, Tome 49 (1999) no. 1, pp. 95-115

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Classification : 60G60, 62M30, 62M40 
Mohapl, Jaroslav. On estimation in random fields generated by linear stochastic partial differential equations. Mathematica slovaca, Tome 49 (1999) no. 1, pp. 95-115. http://geodesic.mathdoc.fr/item/MASLO_1999_49_1_a11/
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[1] AL-GWAIZ M. A.: Theory of Distributions. Marcel Dekker, Inc., New York-Basel-Hong Kong, 1992. | MR | Zbl

[2] CURTAIN R. F.-FALB P. L.: Stochastic differential equations in Hilbert space. J. Differential Equations 10 (1971), 412-130. | MR | Zbl

[3] FLORENS-ZMIROU D.: On estimating the diffusion coefficient from discrete observations. J. Appl. Probab. 30 (1993), 790-804. | MR | Zbl

[4] HUEBNER M.-ROZOVSKII B. L.: On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's. Probab. Theory Related Fields 103 (1995), 143-163. | MR | Zbl

[5] ITO K.: Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. SIAM, Philadelphia, Pennsylvania, 1984. | MR | Zbl

[6] JONES R. H.-VECCHIA A. V.: Fitting Continuous ARM A models to unequally spaced spatial data. J. Amer. Statist. Assoc. 88 (1993), 947-954.

[7] LIPTSER R. S.-SHIRYAYEV A. N.: Statistics of Random Processes I. General Theory. (2nd ed., 1st ed. 1977), Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1984. | MR | Zbl

[8] MARTIN R. J.: The use of time-series models and methods in the analysis of agricultural field trials. Comm. Statist. Theory Methods 19 (1990), 55-81. | MR

[9] MOHAPL J.: A stochastic advection-diffusion model for the rocky flats soil plutonium data. Ann. Inst. Statist. Math. (1999) (To appear). | MR

[10] MOHAPL J.: Discrete sample estimation for Gaussian random fields generated by stochastic partial differential equations. Comm. Statist. Stochastic Models 14 (1998), 883-903. | MR | Zbl

[11] MOHAPL J.: On estimation in the planar Ornstein-Uhlenbeck process. Comm. Statist. Stochastic Models 13 (1997), 435-455. | MR | Zbl

[12] MOHAPL J.: Maximum likelihood estimation in linear infinite dimensional models. Comm. Statist. Stochastic Models 10 (1994), 781-794. | MR | Zbl

[13] NAMACHCHIVAYA N. S.: Stochastic Structural Dynamics. Proceedings of the Symposium held at the University of Illinois at Urbana Champaign October 30. -November 1, 1988. (N. S. Namachchivaya, H. H. Hilton, Y. K. Wen, eds.), University of Illinois at Urbana Champaign, Urbana, Illinois, 1989.

[14] PARTHASARATHY K. R.: Introduction to Probability and Measure. MacMillan Co., India, 1977. | MR | Zbl

[15] PIETERBARG L.-ROZOVSKII B.: Estimating unknown parameters in SPDE's under discrete observations in time. Preprint, 1996.

[16] WALSH J. B.: An introduction to differential equations. In: Lecture Notes in Math. 1180, Springer Verlag, Berlin-New York-Heidelberg, 1986, pp. 266-437. | MR

[17] WHITTLE P.: Topographic correlation, power law covariance functions and diffusion. Biometrika49 (1962), 305-314. | MR | Zbl

[18] YAGLOM A. M.: Some classes of random fields in n-dimensional space related to stationary random processes. Theory Probab. Appl. 3 (1957), 273-320.

[19] YOSIDA K.: Functional Analysis. (4th ed.), Springer-Verlag, New York-Berlin-Heidelberg, 1974. | MR | Zbl