We consider a class of linear systems in state-space form whose parameters evolve in time according to a continuous-time Gauss-Markov process. Our problem is to identify the system from a finite set of noisy output measurements. We derive a connection between this problem and Tikhonov regularization in reproducing kernel Hilbert spaces. Relying upon this result, conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out. Simulated data are used to test the goodness of the proposed approach.