Explicit form of global solution to stochastic logistic differential equation and related topics

Abstract

This paper presents the explicit form of positive global solution to stochastically perturbed nonautonomous logistic equation where w(t) is the standard one-dimensional Wiener process,ν(t, A) = ν(t, A) − tΠ(A), ν(t, A) is the Poisson measure, which is independent on w(t), E[ν(t, A)] = tΠ(A), Π(A) is a finite measure on the Borel sets in R. If coefficients a(t), b(t), α(t) and γ(t, z) are continuous on t, T -periodic on t functions, a(t) > 0, b(t) > 0 andthen there exists unique, positive T -periodic solution to equation for E[1/N (t)].

A Note on a Strong Persistence of Stochastic Predator-Prey Model with Jumps

“…So it is natural to introduce Poisson noises into the population model for describing such discontinuous systems. It is worth noting that the impact of centered and non-centered Poisson noises to the stochastic non-autonomous logistic model and to the stochastic two-species mutualism model is studied in the papers [9] - [12].…”

Dynamics of the Predator-Prey Model with Beddington-DeAngelis Functional Response Perturbed by Lévy Noise

“…So, we take into account not only "small" jumps, corresponding to the centered Poisson measure, but also the "large" jumps, corresponding to the noncentered Poisson measure. It is worth noting that the impact of centered and non-centered Poisson noises to the stochastic non-autonomous logistic model and to the stochastic two-species mutualism model is studied in the papers [5] - [8].…”