Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Asymptotic behavior of the solution to the non-autonomous stochastic logistic differential equation
O. D. Borysenko, D. O. Borysenko
Abstract: It is investigated the non-autonomous logistic differential equation with disturbance of coefficients by white noise, centered and non-centered Poisson noises. The existence of unique global non-negative solution is proved. The sufficient conditions for the population extinction a.s., non-persistence of the population in the mean a.s., weak persistence of the population a.s. are obtained.
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