Minimum distance estimator for a hyperbolic stochastic partial differentialequation

Vincent Monsan; Modeste N'zi

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 2, page 225-238
  • ISSN: 1233-7234

Abstract

top
We study a minimum distance estimator in L 2 -norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.

How to cite

top

Monsan, Vincent, and N'zi, Modeste. "Minimum distance estimator for a hyperbolic stochastic partial differentialequation." Applicationes Mathematicae 27.2 (2000): 225-238. <http://eudml.org/doc/219270>.

@article{Monsan2000,
abstract = {We study a minimum distance estimator in $L_2$-norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.},
author = {Monsan, Vincent, N'zi, Modeste},
journal = {Applicationes Mathematicae},
keywords = {random fields; stochastic partial differential equations; small noise; minimum distance estimator},
language = {eng},
number = {2},
pages = {225-238},
title = {Minimum distance estimator for a hyperbolic stochastic partial differentialequation},
url = {http://eudml.org/doc/219270},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Monsan, Vincent
AU - N'zi, Modeste
TI - Minimum distance estimator for a hyperbolic stochastic partial differentialequation
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 2
SP - 225
EP - 238
AB - We study a minimum distance estimator in $L_2$-norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.
LA - eng
KW - random fields; stochastic partial differential equations; small noise; minimum distance estimator
UR - http://eudml.org/doc/219270
ER -

References

top
  1. H. Dietz and Y. Kutoyants (1992), A minimum-distanceestimator for diffusion processes with ergodic properties, Tech. Report 11, Inst. Appl. Analysis and Stochastics,Berlin. 
  2. H. Dietz and Y. Kutoyants (1997), A class of minimum-distanceestimators for diffusion processes with ergodic properties, Statistics and Decisions 15, 211-217. Zbl0921.62101
  3. M. Dozzi (1989), Stochastic Processes with a Multidimensional Parameter, Longman Sci. Tech. Zbl0663.60039
  4. M. Farré and D. Nualart (1993), Nonlinear stochastic integral equations in the plane, Stochastic Process. Appl. 46, 219-239. Zbl0777.60052
  5. X. Guyon and B. Prum (1981), Semimartingales à deux indices, Ph.D. Thesis, Univ. de Paris VI. Zbl0461.60066
  6. S. Hénaff (1995), On minimum distance estimate of theparameter of the Ornstein-Uhlenbeck process, preprint, Univ. of Angers. 
  7. H. Korezlioglu, G. Mazziotto and J. Szpirglas (1983), Nonlinear filtering equations for two parameter semimartingales, Stochastic Process. Appl. 15, 239-269. Zbl0516.60061
  8. Y. Kutoyants (1994), Identification of Dynamical Systems with Small Noise, Kluwer, Dordrecht. Zbl0831.62058
  9. Y. Kutoyants and O. Lessi (1995), Minimum distance estimation for diffusion random fields, Publ. Inst. Statist. Univ. Paris 29, fasc. 3, 3-20. Zbl0837.62073
  10. Y. Kutoyants, A. Nercessian and P. Pilibossian (1994), On limit distribution of the minimum sup norm estimate of the parameter ofthe Ornstein-Uhlenbeck process, Romanian J. Pure Appl. Math. 39, 119-139. Zbl0813.62075
  11. Y. Kutoyants and P. Pilibossian (1994), On minimum L 1 estimate of the parameter of the Ornstein-Uhlenbeck process, Statist. Probab. Lett. 20, 117-123. Zbl0802.62081
  12. J. Norris (1995), Twisted sheets, J. Funct. Anal. 132, 273-334. Zbl0848.60055
  13. C. Rovira and M. Sanz-Solé (1995), A nonlinear hyperbolic SPDE: Aproximations and support, in: London Math. Soc. Lecture Note Ser. 216, Cambridge Univ. Press, 241-261. Zbl0828.60042
  14. C. Rovira and M. Sanz-Solé (1996), The law of thesolution to a nonlinear hyperbolic SPDE, J. Theoret. Probab. 9, 863-901. Zbl0878.60040

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.