On consistency of minimal distance estimate for diffusion observations
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1991), pp. 11-16.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with the problem of the $\theta$-parameter estimation of the $S (\cdot)$ function (drift coefficient), where it is unknown, by observations of diffusion processes. The method of minimal distance estimation, which allows to construct consistency and asymptotic normality to the estimation of parameter of drift coefficient when $\varepsilon\to 0)$, is discussed.
@article{UZERU_1991_1_a1,
     author = {A. M. Ebady and Yu. A. Kutoyants},
     title = {On consistency of minimal distance estimate for diffusion observations},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {11--16},
     publisher = {mathdoc},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_1991_1_a1/}
}
TY  - JOUR
AU  - A. M. Ebady
AU  - Yu. A. Kutoyants
TI  - On consistency of minimal distance estimate for diffusion observations
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 1991
SP  - 11
EP  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_1991_1_a1/
LA  - ru
ID  - UZERU_1991_1_a1
ER  - 
%0 Journal Article
%A A. M. Ebady
%A Yu. A. Kutoyants
%T On consistency of minimal distance estimate for diffusion observations
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 1991
%P 11-16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_1991_1_a1/
%G ru
%F UZERU_1991_1_a1
A. M. Ebady; Yu. A. Kutoyants. On consistency of minimal distance estimate for diffusion observations. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1991), pp. 11-16. http://geodesic.mathdoc.fr/item/UZERU_1991_1_a1/

[1] Yu. A. Kutoyants, Parameter Estimation for Stochastic Processes, Heldermann, Berlin, 1984 | MR | Zbl

[2] I. A. Ibragimov, R. Z. Khasminskii, Asimptoticheskaya teoriya otsenivaniya, Nauka, M., 1975

[3] R. Sh. Liptser, A. N. Shiryaev, Statistika sluchainykh protsessov, Nauka, M., 1974 | MR | Zbl

[4] Yu. A. Kutoyants, “On nonparametric estimation of the trend coefficient of diffusion process in statist. and control of stochastic processe”, Steklov Seminar, Optimization Software, New York, 1984, 230–250 | MR

[5] A. D. Ventsel, M. I. Freidlin, Fluktuatsii v dinamicheskikh sistemakh, Nauka, M., 1979 | MR

[6] P. W. Millar, “The minimax principle in asymptotic statistical theory”, Lecture notes in mathematics, 976 (1983), 76–265 | MR