Open AccessEstimation of diffusion parameter for stochastic heat equation with white noise
Author(s) -
Diana Avetisian,
Georgiy Shevchenko
Publication year - 2018
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2018/3.1
Subject(s) - stochastic differential equation , heat equation , mathematics , stochastic partial differential equation , white noise , diffusion , mathematical analysis , diffusion equation , sigma , differential equation , partial differential equation , physics , statistics , thermodynamics , economy , service (business) , quantum mechanics , economics
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.