基于年龄结构带跳与分数Brown运动种群系统数值解的均方散逸性

Mean-square Dissipativity of Numerical Methods for A Class of Stochastic Age-dependent Population with Fractional Brown Motion and Poisson Jump

讨论了一类基于年龄结构的带跳与分数Brown运动的种群系统数值解的均方散逸性.在一定条件下,利用It?公式、Cauchy-Schwarz不等式和Bwllman-Gronwall-Type估计等证明了所讨论的系统具有均方散逸性.然后讨论了利用分步倒向Euler方法和带补偿的倒向Euler方法得到的数值解的均方散逸性,并给出详细的证明,得到两种数值方法保留了原方程的散逸特性.

A class of stochastic age-dependent population with fractional Brown motion and Poisson jump is considered.By using It？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.