Estimation of the drift parameter for the fractional stochastic heat equation via power variation

Zeina Mahdi Khalil, Ciprian Tudor
2019 Modern Stochastics: Theory and Applications  
We define power variation estimators for the drift parameter of the stochastic heat equation with the fractional Laplacian and an additive Gaussian noise which is white in time and white or correlated in space. We prove that these estimators are consistent and asymptotically normal and we derive their rate of convergence under the Wasserstein metric.
doi:10.15559/19-vmsta141 fatcat:3oxwmsmrx5fv5gcuicglddbejy