Statistical estimates of parameters of the heat equation with random initial conditions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.62087
author: N. O. Burykina
author: M. M. Leonenko
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 1646743
zbMATH Keywords: heat equation
zbMATH Keywords: random initial conditions
zbMATH Keywords: statistical parameter estimation
MaRDI profile type: Publication
title: Statistical estimates of parameters of the heat equation with random initial conditions
published in: Teoriya Ĭmovirnosteĭ ta Matematychna Statystyka
review text: 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.
description: scientific article; zbMATH DE number 1646743