Optimal Berry-Esseen bound for parameter estimation of SPDE with small noise
Tóm tắt
We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter θ appearing in parabolic SPDEs of the form $$d{u^\varepsilon }(t,x) = ({A_0} + \theta {A_1}){u^\varepsilon }(t,x)dt + \varepsilon dW(t,x),$$ where A0 and A1 are partial differential operators, W is a cylindrical Brownian motion (CBM) and ε ↓ 0. We find an optimal Berry-Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.
Tài liệu tham khảo
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