| 随机脉冲泛函微分方程的{\boldmath p}阶矩有界性 |
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| 引用本文： | 吴述金,宋琼,郭小林.随机脉冲泛函微分方程的{\boldmath p}阶矩有界性[J].数学物理学报(A辑),2010,30(1):126-141. |
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| 作者姓名： | 吴述金 宋琼 郭小林 |
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| 作者单位： | 吴述金,宋琼(华东师范大学金融与统计学院统计与精算学系,上海,200241);郭小林(安徽财经大学信息工程学院计算机系,安徽蚌埠,233041) |
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| 基金项目： | 国家自然科学基金，国家教育部博士点专项基金，上海市自然科学基金 |
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| 摘 要： | 随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型. 该文利用带Razumikhin条件的Liapunov直接法和比较原理, 得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终) p阶矩有界的充分条件, 其中在获得一致有界性和一致最终有界性时, 对dV(t, x(t))/dt 的限制条件也较少, 因此研究结果非常便于应用.
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| 关 键 词： | 微分方程 随机脉冲 一致有界 最终有界 Liapunov方程 Razumikhin条件 |
| 收稿时间： | 2008-03-08 |
| 修稿时间： | 2009-01-20 |
p-Moment Boundedness of Functional Differential Equations with Random Impulses |
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| WU Shu-Jin,SONG Qiong,GUO Xiao-Lin.p-Moment Boundedness of Functional Differential Equations with Random Impulses[J].Acta Mathematica Scientia,2010,30(1):126-141. |
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| Authors: | WU Shu-Jin SONG Qiong GUO Xiao-Lin |
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| Institution: | Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University, Shanghai 200241 |
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| Abstract: | Random impulsive functional differential equation is a mathematical model with extensive applications.By means of Liapunov's direct method coupled with Razumikhin technique and comparison principle,some sufficient conditions for uniformly(uniformly and ultimately, uniformly and uniformly ultimately) p-moment boundedness of such systems are presented, where(dV(t,x(t)))/(dt)is imposed only on a little restriction even to obtain uniform boundedness and uniformly ultimate boundedness.Thus the obtained results a... |
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| Keywords: | Functional differential equation Random impulses Uniform boundedness Ulti-mate boundedness Liapunov function Razumikhin condition |
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