Abstract
The paper considers Kolmogorov–Feller equation for the probability density of a Markov process on a half-axis, which arises in important problems of biology. This process consists of random jumps distributed according to the Laplace law and a deterministic return to zero. It is shown that the Green 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 finding explicit solutions to the Kolmogorov–Feller equation for many initial data.
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Funding
The work is supported by the Russian Science Foundation, project no. 23–11–00056.
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Translated by E. Oborin
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Rozanova, O.S. On the Solution to the Kolmogorov-Feller Equation Arising in a Biological Evolution Model. Moscow Univ. Math. Bull. 78, 276–280 (2023). https://doi.org/10.3103/S0027132223060062
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DOI: https://doi.org/10.3103/S0027132223060062