Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet

We will study the least square estimator θ̂T,S for the drift parameter θ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation Xt,s=−θ∫0t∫0sXv,udvdu+Bt,sα,β,(t,s)∈[0,T]×[0,S]. driven by the fractional Brownian sheet Bα,β with Hurst parameters α,β in (12,58). Using the properties of multiple Wiener-Itô integrals we prove that the estimator is strongly consistent for the parameter θ. In contrast to the one-dimensional case, the estimator θ̂T,S is not asymptotically normal.