Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale

被引：1
|
作者：
Li, Jun-Gang [1 ]
Zheng, Shi-Qing [1 ]
机构：
[1] North China Univ Technol, Dept Stat, Beijing 100144, Peoples R China
来源：
4TH ANNUAL INTERNATIONAL CONFERENCE ON INFORMATION TECHNOLOGY AND APPLICATIONS (ITA 2017) | 2017年 / 12卷
关键词：
D O I：
10.1051/itmconf/20171203002
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued square integrable martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and set-valued square integrable martingale integral equation. The existence and uniqueness of solution to set-valued stochastic integral equation are proved. The discussion will be useful in optimal control and mathematical finance in psychological factors.
引用
收藏
页数：5
相关论文
共 50 条
  • [1] Set-Valued Square Integrable Martingales and Stochastic Integral
    Li, Shoumei
    [J]. COMBINING SOFT COMPUTING AND STATISTICAL METHODS IN DATA ANALYSIS, 2010, 77 : 411 - 417
  • [2] Stochastic integral with respect to set-valued square integrable martingales
    Li, Shoumei
    Li, Jungang
    Li, Xiaohua
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 370 (02) : 659 - 671
  • [3] Set-Valued Stochastic Integrals with Respect to a Real Valued Martingale
    Zhang, Jinping
    [J]. SOFT METHODS FOR HANDLING VARIABILITY AND IMPRECISION, 2008, 48 : 253 - 259
  • [4] Integrable boundedness of set-valued stochastic integrals
    Kisielewicz, Michal
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 481 (02)
  • [5] The Space of Fuzzy Set-Valued Square Integrable Martingales
    Li, Jungang
    Li, Shoumei
    Xue, Yanping
    [J]. 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 2009, : 872 - 876
  • [6] SET-VALUED MEASURES AND SET-VALUED INTEGRALS
    BYRNE, CL
    [J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (06): : A588 - A588
  • [7] On set-valued stochastic integrals
    Jung, EJ
    Kim, JH
    [J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (02) : 401 - 418
  • [8] SET-VALUED MEASURE AND FUZZY SET-VALUED MEASURE
    ZHANG, WX
    LI, T
    MA, JF
    LI, AJ
    [J]. FUZZY SETS AND SYSTEMS, 1990, 36 (01) : 181 - 188
  • [9] Martingale representation theorem for set-valued martingales
    Kisielewicz, Michal
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (01) : 111 - 118
  • [10] On Set-Valued Stochastic Differential Equation of Jump Type
    Zhang, Jinping
    Ogura, Yukio
    [J]. PROCEEDING OF THE 10TH INTERNATIONAL CONFERENCE ON INTELLIGENT TECHNOLOGIES, 2009, : 493 - 499
12345