Estimation problems for coefficients of stochastic partial differential equations. Part II
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 526-554
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As in Part I (see [I. A. Ibragimov and R. Z. Khas'minskii, Theory Probab. Appl., 43 (1999), pp. 370–387]), we consider the problem of estimation of functional parameters $a_k(t,x),\theta(t,x)$ by observing a solution $u_\varepsilon(t,x)$ of a stochastic partial differential equation $$ du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon+\theta\,dt+\varepsilon\,dw(t), $$ where $w(t)$ is a Wiener process. We investigate problems of the existence of consistent estimates for $\theta$ and their rate of convergence to $\theta$ dependent on properties of the functional class $\Theta$, which a priori contains $\theta$.
Keywords:
inverse problems, stochastic differential equations, statistical estimation, nonparametric estimating problems.
@article{TVP_1999_44_3_a2,
author = {I. A. Ibragimov and R. Z. Khas'minskii},
title = {Estimation problems for coefficients of stochastic partial differential equations. {Part~II}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {526--554},
year = {1999},
volume = {44},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a2/}
}
TY - JOUR AU - I. A. Ibragimov AU - R. Z. Khas'minskii TI - Estimation problems for coefficients of stochastic partial differential equations. Part II JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1999 SP - 526 EP - 554 VL - 44 IS - 3 UR - http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a2/ LA - ru ID - TVP_1999_44_3_a2 ER -
%0 Journal Article %A I. A. Ibragimov %A R. Z. Khas'minskii %T Estimation problems for coefficients of stochastic partial differential equations. Part II %J Teoriâ veroâtnostej i ee primeneniâ %D 1999 %P 526-554 %V 44 %N 3 %U http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a2/ %G ru %F TVP_1999_44_3_a2
I. A. Ibragimov; R. Z. Khas'minskii. Estimation problems for coefficients of stochastic partial differential equations. Part II. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 526-554. http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a2/