Parameter estimation for the stochastic Burgers equation driven by white noise from local measurements

For one dimensional stochastic Burgers equation driven by space-time white noise we consider the problem of estimation of the diffusivity parameter in front of the second-order spatial derivative. Based on local observations in space, we study the estimator derived in [Altmeyer, Rei{\ss}, Ann. Appl. Probab.(2021)] for linear stochastic heat equation that has also been used in [Altmeyer, Cialenco, Pasemann, Bernoulli (2023)] to cover large class of semilinear SPDEs and has been examined for the stochastic Burgers equation driven by trace class noise. We extend the achieved results by considering the space-time white noise case which has also relevant physical motivations. After we establish new regularity results for the solution, we are able to show that our proposed estimator is strongly consistent and asymptotically normal.