  The kangaroo process (KP) is characterized by various forms of the covariance
and can serve as a useful model of random noises. We discuss properties of that
process for the exponential, stretched exponential and algebraic (power-law)
covariances. Then we apply the KP as a model of noise in the generalized
Langevin equation and simulate solutions by a Monte Carlo method. Some results
appear to be incompatible with requirements of the fluctuation-dissipation
theorem because probability distributions change when the process is inserted
into the equation. We demonstrate how one can construct a model of noise free
of that difficulty. This form of the KP is especially suitable for physical
applications.
