# Minimum distance estimator for a hyperbolic stochastic partial differentialequation

Applicationes Mathematicae (2000)

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

## Access Full Article

top## Abstract

top## How to cite

topMonsan, 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- H. Dietz and Y. Kutoyants (1992), A minimum-distanceestimator for diffusion processes with ergodic properties, Tech. Report 11, Inst. Appl. Analysis and Stochastics,Berlin.
- 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
- M. Dozzi (1989), Stochastic Processes with a Multidimensional Parameter, Longman Sci. Tech. Zbl0663.60039
- M. Farré and D. Nualart (1993), Nonlinear stochastic integral equations in the plane, Stochastic Process. Appl. 46, 219-239. Zbl0777.60052
- X. Guyon and B. Prum (1981), Semimartingales à deux indices, Ph.D. Thesis, Univ. de Paris VI. Zbl0461.60066
- S. Hénaff (1995), On minimum distance estimate of theparameter of the Ornstein-Uhlenbeck process, preprint, Univ. of Angers.
- H. Korezlioglu, G. Mazziotto and J. Szpirglas (1983), Nonlinear filtering equations for two parameter semimartingales, Stochastic Process. Appl. 15, 239-269. Zbl0516.60061
- Y. Kutoyants (1994), Identification of Dynamical Systems with Small Noise, Kluwer, Dordrecht. Zbl0831.62058
- 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
- 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
- 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
- J. Norris (1995), Twisted sheets, J. Funct. Anal. 132, 273-334. Zbl0848.60055
- 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
- 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 ?

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