Estimation of diffusion parameter for stochastic heat equation with white noise

Abstract

This paper deals with stochastic differential heat equation which is the typical example of stochastic partial differential equations (SPDE). In particular, paper is devoted to the estimation of diffusion parameter $\sigma$ for the random field which is the solution of stochastic differential heat equation for R^d, d = 1, 2, 3. The estimtion of diffusion parameter was constructed in accordance with observations on the grid. It was shown that the constructed estimate is strictly consistent and asymptotically normal, the asymptotic variance was calculated.