Geodesic
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},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a2/}
}
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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/