Planning Planning of experiments for a nonautonomous Ornstein-Uhlenbeck process

Abstract

We study exact optimal designs for processes governed by mean-reversion stochastic differential equations with a time dependent volatility and known mean-reversion speed. It turns out that any mean-reversion Itō process has a product covariance structure. We prove the existence of a nondegenerate optimal sampling design for the parameter estimation and derive the information matrix corresponding to the observation of the full path. The results are demonstrated on a process with exponential volatility.