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.

A special class of random nonstationary processes on Poisson point flows with piecewiseconstant and piecewise-linear trajectories is considered in the paper. Expressions for mean values of these processes are obtained as functions of time.

A numerical stochastic model of spatio-temporal inhomogeneous fields of daily sums of liquid precipitation is considered in the paper on regular and irregular grids. The approach to modelling inhomogeneous fields is based on stochastic interpolation of fields from weather stations to grid points.

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