Parameter estimation from local measurements for a class of stochastic Burgers equations

We deal with a class of semilinear SPDEs driven by space–time white noise that includes the one dimensional stochastic Burgers equation. Such equations can have nonlocal and quadratic nonlinearities. 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 (Ann. Appl. Probab. 31 (2021) 1–38) for linear stochastic heat equation that has also been used in (Bernoulli 29 (2023) 2035–2061) to cover certain class of semilinear SPDEs including stochastic Burgers equations driven by trace class noise. The space-time white noise case we consider 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.