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

DOI10.3103/S0027132223060062arXiv2305.16010OpenAlexW4393126242MaRDI QIDQ6437963

Olga S. Rozanova

Publication date: 25 May 2023

Abstract: 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 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 explicitly find solutions to the Kolmogorov-Feller equation for many initial data.

Full work available at URL: https://doi.org/10.3103/s0027132223060062

Mathematics Subject Classification ID

Problems related to evolution (92D15) Continuous-time Markov processes on general state spaces (60J25)

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