数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 126-141.

• 论文 • 上一篇    下一篇

随机脉冲泛函微分方程的{\boldmath p}阶矩有界性

吴述金, 宋琼, 郭小林   

  1. 华东师范大学 金融与统计学院 统计与精算学系 上海 200241
  • 收稿日期:2008-03-08 修回日期:2009-01-20 出版日期:2010-01-01 发布日期:2010-01-01
  • 基金资助:

    国家自然科学基金(10771070)、国家教育部博士点专项基金(20060269016)、上海市自然科学基金(08ZR1407000)资助.

p-Moment Boundedness of Functional Differential Equations with Random Impulses

WU Shu-Jin, SONG Qiong, GUO Xiao-Lin   

  1. Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University, Shanghai 200241
  • Received:2008-03-08 Revised:2009-01-20 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(10771070)、国家教育部博士点专项基金(20060269016)、上海市自然科学基金(08ZR1407000)资助.

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.

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

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 are very convenient to apply.

Key words: Functional differential equation, Random impulses, Uniform boundedness, Ultimate boundedness, Liapunov function, Razumikhin condition

中图分类号: 

  • 34K20