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The kangaroo process (KP) is characterized by various forms of the covarianceand can serve as a useful model of random noises. We discuss properties of thatprocess for the exponential, stretched exponential and algebraic (power-law)covariances. Then we apply the KP as a model of noise in the generalizedLangevin equation and simulate solutions by a Monte Carlo method. Some resultsappear to be incompatible with requirements of the fluctuation-dissipationtheorem because probability distributions change when the process is insertedinto the equation. We demonstrate how one can construct a model of noise freeof that difficulty. This form of the KP is especially suitable for physicalapplications.Comment: 22 pages (RevTeX) and 4 figure

Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation