In the publication of F.Dunker and T.Hohage we have studied, we do not only find the general convergence rate result we proved in theorem 4.5, but also an application of the theory to a specific ill-posed problem, namely parameter identification of the stationary version of an SDE. We want to examine this problem and to extend the result to a related situation in which we do take time into account. First let us give some context to the situation with an interesting problem motivated by research in biology.