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A model of asymptotically stationary piecewise-linear random processes based on homogeneous Poisson flows is considered in the paper. Exact expressions for the mathematical expectation and variance as functions of a continuous argument are presented. A model of asymptotically periodically correlated piecewise-constant non-Gaussian random processes is also presented. This model is based on inhomogeneous Poisson flows of special form.

Stochastic models of piecewise-constant and piecewise-linear non-Gaussian processes based on Poisson flows