一类泛函集值随机微分方程的解
The Solution of a Type of Functional Set-Valued Stochastic Differential Equation
DOI: 10.12677/AAM.2019.812218, PDF,   
作者: 李俊刚, 薛 竹:北方工业大学理学院,北京
关键词: 泛函集值方程存在性唯一性Functional Set-Valued Equation Solution Existence Uniqueness
摘要: 本文介绍了集值及其性质,泛函集值随机微分方程,在给定初值的情况下,给出了一类泛函集值随机微分方程的强解的存在性和唯一性的证明。
Abstract: In this paper, we shall introduce set-valued and its properties, and discuss the functional set-valued stochastic differential equation. When the initial value is given, we shall prove the existence and uniqueness of solution of the type of functional set-valued stochastic differential equation.
文章引用:李俊刚, 薛竹. 一类泛函集值随机微分方程的解[J]. 应用数学进展, 2019, 8(12): 1881-1884. https://doi.org/10.12677/AAM.2019.812218

参考文献

[1] 蒲兴成, 张毅. 随机微分方程及其在数理金融中的应用[M]. 北京: 科学出版社, 2010.
[2] 厄克森达尔, 刘金山, 吴付科. 随机微分方程导论与应用[M]. 北京: 科学出版社, 2012.
[3] Mao, X.R. (2003) Numerical Solutions of Stochastic Functional Differential Equations. Journal of Computation and Mathematics, 6, 141-161.
[Google Scholar] [CrossRef
[4] Li, S.M., Ogura, Y. and Kreinovich, V. (2002) Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Springer, Dordrecht.
[Google Scholar] [CrossRef
[5] Li, J.G. and Li, S.M. (2009) Ito Type Set-Valued Stochastic Differential Equation. Journal of Uncertain Systems, 3, 52-63.
[6] Li, S.M., Li, J.G. and Li, X.H. (2010) Stochastic Integral with Respect to Set-Valued Square Integrable Martingales. Journal of Mathematical Analysis and Applications, 370, 659-671.
[Google Scholar] [CrossRef