Estimation of diffusion parameter for stochastic heat equation with white noise
DOI:
https://doi.org/10.17721/1812-5409.2018/3.1Abstract
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.
Key words: stochastic partial differential equations, stochastic differential heat equation, estimate, asymptotical normality, consistency.
Pages of the article in the issue: 9 - 16
Language of the article: English
References
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M. TAYLOR, Random Fields: Stationarity, Ergodicity, and Spectral Behavior, http://www.unc.edu/math/Faculty/met/rndfcn.pdf.
D. NUALART, G. PECCATI, (2005) Central limit theorems for sequences of multiple stochastic integrals, The Annals of Probability, 177-193.
J. POSPISIL, R. TRIBE, (2014) Parameter Estimates and Exact Variations for Stochastic Heat Equations Driven by Space-Time White Noise, Stochastic Analysis and Applications, 593-611.
L. ISSERLIS, (1918) On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika, 134-139.
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