Convergence of the Stochastic Age-Structured Population System with Diffusion

In this paper, stochastic age-structure population system with jump are studied. It is proved that the semi-implicit Euler approximation solutions converge to the analytic solution for the stochastic age-structured population system with Poisson jump. The analysis use Ito′s formula, Burkholder-Davis-Gundy’s inequality, Gronwall’s lemma and some inequalities for our purposes.