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.

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The paper presents results of numerical studies of stochastic properties of time series of the enthalpy of humid air and the heat index characterizing the heat content and thermal effects of humid air on human beings. The study was based on real meteorological observations and stochastic model of joint time series for surface air temperature and relative humidity taking into account daily course of real meteorological processes.

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