  We consider the problem of predicting values of a random process or field
satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where
errors $\varepsilon(x)$ are correlated. This is a common problem in kriging,
where the case of discrete observations is standard. By focussing on the case
of continuous observations, we derive expressions for the best linear unbiased
predictors and their mean squared error. Our results are also applicable in the
case where the derivatives of the process $y$ are available, and either a
response or one of its derivatives need to be predicted. The theoretical
results are illustrated by several examples in particular for the popular
Mat\'{e}rn $3/2$ kernel.
