Statistical estimates of parameters of the heat equation with random initial conditions
This paper deals with the classical homogeneous one-dimensional heat equation with random initial conditions which are real separable mean-square continuous and a.s. continuous wide sense stationary random processes. The paper is devoted to the statistical aspects of the problem of parameter estimation, namely, obtaining the estimations of parameters of the heat equation. The conditions of consistency and asymptotic normality of the least contrast parameter estimations of the random fields are given which are re-normalized solutions of the heat equation with the above-mentioned conditions.NEWLINENEWLINENEWLINEThe approach of this paper is based on ideas of work by \textit{N.N. Leonenko} and \textit{W.A. Woyczynski} [Stochastic Processes Appl. 76, No.2, 141-165 (1998; Zbl 0928.35214)], where the same approach is introduced for estimating of parameters of Burgers' equation with random data. Steps of the approach are the following: 1) homogenization and Gaussianization of solutions; 2) discretization of solutions; 3) application of the method of the least contrast unknown parameter estimations of the heat equation.
scientific article; zbMATH DE number 1646743