Ultimate efficiency of experimental designs for Ornstein–Uhlenbeck type processes

For processes governed by linear Itō stochastic differential equations of the form d X ( t ) = [ a ( t ) + b ( t ) X ( t ) ] d t + σ ( t ) d W ( 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.