@article{Borysenko_Borysenko_2017, title={Explicit form of global solution to stochastic logistic differential equation and related topics}, volume={5}, url={http://iapress.org/index.php/soic/article/view/20170305}, DOI={10.19139/soic.v5i1.262}, abstractNote={<p>This paper presents the explicit form of positive global solution to stochastically perturbed nonautonomous logistic equation $$dN(t)=N(t)\left[(a(t)-b(t)N(t))dt+\alpha(t)dw(t)+\int_{\mathbb{R }\gamma(t,z)\tilde u(dt,dz)\right],\ N(0)=N_0,$$ where $w(t)$ is the standard one-dimensional Wiener process, $\tilde u(t,A)= u(t,A)-t\Pi(A)$, $ u(t,A)$ is the Poisson measure, which is independent on $w(t)$, $E[ u(t,A)]=t\Pi(A)$, $\Pi(A)$ is a finite measure on the Borel sets in $\mathbb{R}$. If coefficients $a(t), b(t), \alpha(t)$ and $\gamma(t,z)$ are continuous on $t$, $T$-periodic on $t$ functions, $a(t)&gt;0, b(t)&gt;0$ and $$\int_{0}^{T}\left[a(s)-\alpha^2(s)-\int_{\mathbb{R }\frac{\gamma^2(s,z)}{1+\gamma(s,z)}\Pi(dz)\right]ds&gt;0,$$ then there exists unique, positive $T$-periodic solution to equation for $E[1/N(t)]$.</p&gt;}, number={1}, journal={Statistics, Optimization & Information Computing}, author={Borysenko, Dmytro and Borysenko, Oleksandr}, year={2017}, month={Mar.}, pages={58-64} }