Solutions of the generalized Langevin equation are simulated by using a jumping process as a model of the stochastic force. This force is strongly correlated; we consider two forms of correlations' tail: \sim 1/t2 and \sim 1/\sqrt t. We demonstrate that remnants of the initial condition can be recognized in the velocity probability distributions after a long time if the correlation function falls slowly. Moreover, the system can exhibit both normal and anomalously slow diffusion which is reflected by the structure of the spectra.
PACS numbers: 05.40.--a, 02.50.--r, 05.10.Gg
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