Geodesic
Solution of the Kolmogorov–Feller equation arising in the model of biological evolution
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 23-27 
O. S. Rozanova. Solution of the Kolmogorov–Feller equation arising in the model of biological evolution. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 23-27. http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a3/
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     author = {O. S. Rozanova},
     title = {Solution of the {Kolmogorov{\textendash}Feller} equation arising in the model of biological evolution},
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     pages = {23--27},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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

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