Zhang, Xinjing; Zhang, Qimin Mean-square dissipativity of numerical methods for a class of stochastic age-dependent populations with fractional Brownian motion and Poisson jump. (Chinese. English summary) Zbl 1363.60090 J. Ningxia Univ., Nat. Sci. Ed. 37, No. 1, 11-15, 21 (2016). Summary: A class of stochastic age-dependent population with fractional Brownian motion and Poisson jump is considered. By using Itô formula, Cauchy-Schwarz inequality and Bellman-Gronwall-type estimates, a sufficient condition is established to guarantee the mean-square dissipativity of the system. Finally, it is shown that the mean-square dissipativity is preserved by the split-step backward Euler method and compensated backward Euler method under a step-size constraint. MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 92D25 Population dynamics (general) Keywords:global mean-square dissipativity; Itô formula; compensated backward Euler method; Bellman-Gronwall-type estimates PDFBibTeX XMLCite \textit{X. Zhang} and \textit{Q. Zhang}, J. Ningxia Univ., Nat. Sci. Ed. 37, No. 1, 11--15, 21 (2016; Zbl 1363.60090)