Estimation problems for coefficients of stochastic partial differential equations. Part III
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 209-235
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This paper is concerned with the problem of estimating a functional parameter $a_0(t,x)$ upon observation of a solution $u_\varepsilon(t,x)$ of the stochastic partial differential equation $$ du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon\,dt+f\,dt+\varepsilon\,dw(t)=0. $$ Asymptotically minimax estimates for $a_0$ and asymptotically effective estimates for $\Phi(a_0)$ are found under the assumption that $a_0$ is independent of $t$.
Keywords:
inverse problems, stochastic partial differential equations, statistical estimation, nonparametric problems of estimating.
@article{TVP_2000_45_2_a0,
author = {I. A. Ibragimov and R. Z. Khas'minskii},
title = {Estimation problems for coefficients of stochastic partial differential equations. {Part~III}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {209--235},
year = {2000},
volume = {45},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a0/}
}
TY - JOUR AU - I. A. Ibragimov AU - R. Z. Khas'minskii TI - Estimation problems for coefficients of stochastic partial differential equations. Part III JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2000 SP - 209 EP - 235 VL - 45 IS - 2 UR - http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a0/ LA - ru ID - TVP_2000_45_2_a0 ER -
%0 Journal Article %A I. A. Ibragimov %A R. Z. Khas'minskii %T Estimation problems for coefficients of stochastic partial differential equations. Part III %J Teoriâ veroâtnostej i ee primeneniâ %D 2000 %P 209-235 %V 45 %N 2 %U http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a0/ %G ru %F TVP_2000_45_2_a0
I. A. Ibragimov; R. Z. Khas'minskii. Estimation problems for coefficients of stochastic partial differential equations. Part III. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 209-235. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a0/