Abstract
One-dimensional evolution equations with a linear random parameter, which is a colored-noise stochastic process, are analyzed. Exact analytical expression for the probability distribution of the considered processes is given explicitly. The existence of stationary states and critical properties of the systems are considered. An analytical example is studied. It is shown that there exist a class of one-dimensional non-stationary markovian processes for which the one-dimensional distribution is the same as for the processes of interest.
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