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

作　　者：李强 张启敏 李西宁[2] LI Qiang ZHANG Qimin LI Xining(School of Mathematics and Computer Science, Beifang University for Nationalities, Yinchuan 750021, Ningxia School of Mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]宁夏大学数学与计算机学院,宁夏银川750021

出　　处：《四川师范大学学报（自然科学版）》2017年第5期632-638,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11461053)

摘　　要：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.

关 键 词：分数Brown运动 Bellman-Gronwall型引理 补偿倒向Euler方法 均方散逸 

分 类 号：O241.82[理学—计算数学]