In this paper we construct a kernel estimator of a time-varying coefficient of a strongly elliptic partial differential operator in a stochastic parabolic equation.The equation is assumed diagonalizable; that is, all the operators have a common system of eigenfunctions.The mean-square convergence of the estimator is established. The rate of convergence is determined both by the smoothness of the true coefficient and by the asymptotics of the eigenvalues of the operators in the equation.
"Asymptotic analysis of a kernel estimator for parabolic SPDE's with time-dependent coefficients." Ann. Appl. Probab. 10 (4) 1246 - 1258, November 2000. https://doi.org/10.1214/aoap/1019487615