Stochastic Age-dependent Population System With Diffusion

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is considered. In a first part, we construct a successive iterative sequence of solutions. Using the Bihari's inequality and the Davis's inequality, we can get that it is bounded and converges in I2(0,T;V)∩L2(Ω;C(0,T;H)). Then we obtain the existence and uniqueness of solution for stochastic age-dependent population with diffusion under the non-Lipschitz conditions. In a second part, we study numerical method of stochastic age-dependent population equations with diffusion. When influence of external environment and random perturbation depend on time t, we build a semi-implicit Euler algorithm. With the help of the Hold inequality, the Bihari inequality, the Gronwall inequality and the Burkholder-Davis-Gundy's inequality, we estimate an approximate error in the case when Lipschitz coefficient is a constant.