分数Brown运动随机固定资产模型数值解的均方散逸性

Mean-square Dissipativity of Numerical Methods for Stochastic Age-dependent Capital System with Fractional Brown Motion

讨论一类带分数Brown运动随机固定资产模型数值解的均方散逸性.在一定条件下,根据It?公式和Bellman-Gronwall型引理,得出了模型具有均方散逸性.分别利用分步倒向Euler方法和补偿倒向Euler方法讨论数值解的均方散逸性,并给出数值解散逸存在的充分条件,通过数值算例对所给出的结论进行验证.

In this paper, we introduce a class of stochastic age-dependent capital system with fractional Brown motion. By using It＇s formula and Bellman-Gronwall-type estimates, a sufficient condition is established to guarantee the mean-square dissipativity of this model. Then, 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. Finally, the theoretical result is illustrated by a numerical experiment.