Effective observation of random processes using derivatives

Abstract.

What are optimal observation times of a random process to obtain good prediction or good estimation of the (parametric) trend? In the presented paper we discuss especially the following question: What is better, observation of a differentiable process itself or observation of derivatives of certain degree. We start with simple examples and then we give little bit of theory where observation of derivatives should be preferred. Further, we find some analytical results if the covariance function comes from the Matérn-class or from the J-Bessel-class.