Minimum distance estimator for a hyperbolic stochastic partial differentialequation
Monsan, Vincent ; N'zi, Modeste
Applicationes Mathematicae, Tome 27 (2000), p. 225-238 / Harvested from The Polish Digital Mathematics Library

We study a minimum distance estimator in L2-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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:219270
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     author = {Vincent Monsan and Modeste N'zi},
     title = {Minimum distance estimator for a hyperbolic stochastic partial differentialequation},
     journal = {Applicationes Mathematicae},
     volume = {27},
     year = {2000},
     pages = {225-238},
     zbl = {0992.62077},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i2p225bwm}
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Monsan, Vincent; N'zi, Modeste. Minimum distance estimator for a hyperbolic stochastic partial differentialequation. Applicationes Mathematicae, Tome 27 (2000) pp. 225-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i2p225bwm/

[000] H. Dietz and Y. Kutoyants (1992), A minimum-distanceestimator for diffusion processes with ergodic properties, Tech. Report 11, Inst. Appl. Analysis and Stochastics,Berlin.

[001] H. Dietz and Y. Kutoyants (1997), A class of minimum-distanceestimators for diffusion processes with ergodic properties, Statistics and Decisions 15, 211-217. | Zbl 0921.62101

[002] M. Dozzi (1989), Stochastic Processes with a Multidimensional Parameter, Longman Sci. Tech. | Zbl 0663.60039

[003] M. Farré and D. Nualart (1993), Nonlinear stochastic integral equations in the plane, Stochastic Process. Appl. 46, 219-239. | Zbl 0777.60052

[004] X. Guyon and B. Prum (1981), Semimartingales à deux indices, Ph.D. Thesis, Univ. de Paris VI. | Zbl 0461.60066

[005] S. Hénaff (1995), On minimum distance estimate of theparameter of the Ornstein-Uhlenbeck process, preprint, Univ. of Angers.

[006] H. Korezlioglu, G. Mazziotto and J. Szpirglas (1983), Nonlinear filtering equations for two parameter semimartingales, Stochastic Process. Appl. 15, 239-269. | Zbl 0516.60061

[007] Y. Kutoyants (1994), Identification of Dynamical Systems with Small Noise, Kluwer, Dordrecht. | Zbl 0831.62058

[008] Y. Kutoyants and O. Lessi (1995), Minimum distance estimation for diffusion random fields, Publ. Inst. Statist. Univ. Paris 29, fasc. 3, 3-20. | Zbl 0837.62073

[009] 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. | Zbl 0813.62075

[010] Y. Kutoyants and P. Pilibossian (1994), On minimum L1 estimate of the parameter of the Ornstein-Uhlenbeck process, Statist. Probab. Lett. 20, 117-123. | Zbl 0802.62081

[011] J. Norris (1995), Twisted sheets, J. Funct. Anal. 132, 273-334. | Zbl 0848.60055

[012] 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. | Zbl 0828.60042

[013] C. Rovira and M. Sanz-Solé (1996), The law of thesolution to a nonlinear hyperbolic SPDE, J. Theoret. Probab. 9, 863-901. | Zbl 0878.60040