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The Kolmogorov-Feller equation for the probability density of a Markovprocess on a half-axis, which arises in important problems of biology, isconsidered. This process consists of random jumps distributed according toLaplace's law and a deterministic return to zero. It is shown that Green'sfunction for such an equation can be found both in the form of a series and inexplicit form for some ratios of the parameters. This allows one to explicitlyfind solutions to the Kolmogorov-Feller equation for many initial data.

On the solution of the Kolmogorov-Feller equation arising in the model of biological evolution