Abstract
A problem of estimating a functional parameter θ(x) and functionals Φ(θ) based on observation of a solution u ε(t, x) of the stochastic partial differential equation \(du_\varepsilon (t)= \sum\limits_{|k| \leqslant 2p} a_k D_x^k u_\varepsilon dt+ \theta (x)g(u_\varepsilon,t,x)+\varepsilon dw(t)\) is considered. The asymptotic problem setting, as the noise intensity ε → 0, is investigated.
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Ibragimov, I.A. An Estimation Problem for Quasilinear Stochastic Partial Differential Equations. Problems of Information Transmission 39, 51–77 (2003). https://doi.org/10.1023/A:1023630515274
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DOI: https://doi.org/10.1023/A:1023630515274