一类特殊的集值随机泛函微分方程

基金项目:

国家自然科学基金资助项目(11171010)

北京市自然科学基金资助项目(1112001)

北京工业大学科技基金资助项目(ykj-2012-7771)

详细信息

Special Type of Set-valued Stochastic Functional Differential Equations

College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

摘要: 为研究一类特殊的集值随机泛函微分方程,即漂移项是集值随机过程、扩散项是单值随机过程的集值随机泛函微分方程,给出了此类集值随机泛函微分方程的解的定义,并在Lipschitz连续性条件和线性增长的条件下,利用Picard迭代的方法证明了其解的存在唯一性定理.在此基础上进一步研究了时滞集值随机微分方程及其Caratheodory近似解问题.
- 集值勒贝格积分 /
- 集值随机泛函微分方程 /
- 时滞集值随机微分方程 /
- Caratheodory近似解
Abstract: To investigate a special type of set-valued stochastic functional differential equations which drift coefficient is set-valued stochastic process and diffusion coefficient is single-valued stochastic process,the definition of solutions for this type of equations was introduced,and its existence and uniqueness theorem of solutions was proved under the Lipschitz and linear growth conditions.Set-valued stochastic differential delay equations also were discussed,and in order to develop its applications,the Caratheodary approximate solutions were given.