On estimation in random fields generated by linear stochastic partial differential equations

Jaroslav Mohapl

Mathematica Slovaca (1999)

  • Volume: 49, Issue: 1, page 95-115
  • ISSN: 0232-0525

How to cite

top

Mohapl, Jaroslav. "On estimation in random fields generated by linear stochastic partial differential equations." Mathematica Slovaca 49.1 (1999): 95-115. <http://eudml.org/doc/32136>.

@article{Mohapl1999,
author = {Mohapl, Jaroslav},
journal = {Mathematica Slovaca},
keywords = {maximum likelihood; spatial processes; Schwartz distribution},
language = {eng},
number = {1},
pages = {95-115},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On estimation in random fields generated by linear stochastic partial differential equations},
url = {http://eudml.org/doc/32136},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Mohapl, Jaroslav
TI - On estimation in random fields generated by linear stochastic partial differential equations
JO - Mathematica Slovaca
PY - 1999
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 49
IS - 1
SP - 95
EP - 115
LA - eng
KW - maximum likelihood; spatial processes; Schwartz distribution
UR - http://eudml.org/doc/32136
ER -

References

top
  1. AL-GWAIZ M. A., Theory of Distributions, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1992. (1992) Zbl0759.46033MR1172993
  2. CURTAIN R. F.-FALB P. L., Stochastic differential equations in Hilbert space, J. Differential Equations 10 (1971), 412-130. (1971) Zbl0225.60028MR0303603
  3. FLORENS-ZMIROU D., On estimating the diffusion coefficient from discrete observations, J. Appl. Probab. 30 (1993), 790-804. (1993) Zbl0796.62070MR1242012
  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. (1995) Zbl0831.60070MR1355054
  5. ITO K., Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces, SIAM, Philadelphia, Pennsylvania, 1984. (1984) Zbl0547.60064MR0771478
  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. (1993) 
  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. (1977) Zbl0364.60004MR0474486
  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. (1990) MR1060398
  9. MOHAPL J., A stochastic advection-diffusion model for the rocky flats soil plutonium data, Ann. Inst. Statist. Math. (1999) (To appear). (1999) MR1771482
  10. MOHAPL J., Discrete sample estimation for Gaussian random fields generated by stochastic partial differential equations, Comm. Statist. Stochastic Models 14 (1998), 883-903. (1998) Zbl0903.62076MR1631463
  11. MOHAPL J., On estimation in the planar Ornstein-Uhlenbeck process, Comm. Statist. Stochastic Models 13 (1997), 435-455. (1997) Zbl0891.62059MR1457656
  12. MOHAPL J., Maximum likelihood estimation in linear infinite dimensional models, Comm. Statist. Stochastic Models 10 (1994), 781-794. (1994) Zbl0815.62057MR1298505
  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. (1989) 
  14. PARTHASARATHY K. R., Introduction to Probability and Measure, MacMillan Co., India, 1977. (1977) Zbl0395.28001MR0651012
  15. PIETERBARG L.-ROZOVSKII B., Estimating unknown parameters in SPDE's under discrete observations in time, Preprint, 1996. (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. (1986) MR0876085
  17. WHITTLE P., Topographic correlation, power law covariance functions and diffusion, Biometrika49 (1962), 305-314. (1962) Zbl0114.08003MR0181076
  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. (1957) 
  19. YOSIDA K., Functional Analysis, (4th ed.), Springer-Verlag, New York-Berlin-Heidelberg, 1974. (1974) Zbl0286.46002MR0350358

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.