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We will study the least square estimator $\hat{\theta}_{T,S}$ for the driftparameter $\theta$ of the fractional Ornstein-Uhlenbeck sheet which is definedas the solution of the Langevin equation X_{t,s}= -\theta \int^{t}_{0}\int^{s}_{0} X_{v,u}dvdu + B^{\alpha, \beta}_{t,s}, \qquad (t,s) \in[0,T]\times [0,S] driven by the fractional Brownian sheet $B^{\alpha ,\beta}$with Hurst parameters $\alpha, \beta$ in $(1/2, 5/8)$. Using the properties ofmultiple Wiener-It\^o integrals we prove that the estimator is stronglyconsistent for the parameter $\theta$. In contrast to the one-dimensional case,the estimator $\hat{\theta}_{T,S}$ is not asymptotically normal.

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