Ultimate efficiency of experimental designs for Ornstein-Uhlenbeck type processes

For processes governed by linear Itō stochastic differential equations of the form dX(t)=[a(t)+b(t)X(t)]dt+σ(t)dW(t), we discuss the existence of optimal sampling designs with strictly increasing sampling times. We derive an asymptotic Fisher information matrix, which we take as a reference in assessing the quality of the finite-point sampling designs. The results are extended to a broader class of Itō stochastic differential equations. We give an example based on the Gompertz tumour growth law.