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Under distribution uncertainty, on the basis of discrete data we investigatethe consistency of the least squares estimator (LSE) of the parameter for thestochastic differential equation (SDE) where the noise are characterized by$G$-Brownian motion. In order to obtain our main result of consistency ofparameter estimation, we provide some lemmas by the theory of stochasticcalculus of sublinear expectation. The result shows that under some regularityconditions, the least squares estimator is strong consistent uniformly on theprior set. An illustrative example is discussed.

Consistency of least squares estimation to the parameter for stochastic differential equations under distribution uncertainty