Geodesic
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. 
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     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},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a0/}
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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/