Statistical estimates of parameters of the heat equation with random initial conditions. (English. Ukrainian original) Zbl 0990.62087

Burykina, N. O.; Leonenko, M. M.

Theory Probab. Math. Stat. 61, 3-14 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 3-14 (2000).

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.
The approach of this paper is based on ideas of work by N.N. Leonenko and 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.

Reviewer: Swishchuk, A.V.(Kyïv)

MSC:

62M40	Random fields; image analysis
35R60	PDEs with randomness, stochastic partial differential equations
35L05	Wave equation

Keywords:

heat equation; random initial conditions; statistical parameter estimation

Citations:

Zbl 0928.35214