随机积分和微分方程在弱拓扑下解的存在性和比较结果<sup>*</sup>

丁协平

随机积分和微分方程在弱拓扑下解的存在性和比较结果^*

丁协平

四川师范大学

基金项目: * 中国科学院科学基金资助的课题

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出版历程
- 收稿日期: 1986-07-26
- 刊出日期: 1987-12-15

Existence and Comparison Results of Solutions for Nonlinear Random Integral and Differential Equations Relative to Weak Topology

Ding Xie-ping

Sichuan Normal University, Chengdu

摘要

摘要: 在本文中,我们对非线性随机Volterra积分方程在Banach空间的弱拓扑下的随机解证明了几个存在定理.然后作为应用,我们得到了随机微分方程的弱随机解的存在定理.还得到了这些随机方程的极值随机解的存在性和随机比较定理.我们的定理改进和推广了[4,5,10,11,12]中的相应结果.

Abstract: In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12].

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参考文献(15)

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