LAUSR

Abstract 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 ϵ ( t , x ) = ( A 0 + θ A 1 ) u ϵ ( t , x ) d t + ϵ d W ( t , x ) , where A 0 and A 1 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.