Applied models of random evolutions

The main aim of this article is to present some results in the field of equations for random evolutions and to point out some their possible applications. It is intended first of all to engineers and practical scientists who work in various domains of industry and technology. We consider a mathematical model of one-dimensional random evolution with a constant velocity governed by a Poisson process. The explicit formula for probability density in such a model is given. Two possible practical applications are discussed. The probability of reaching the emergency levels is also given. The planar random evolution with a constant velocity a's considered which may be used for describing the processes of wave spreading in homogeneous media.