| 石学军,冯群,田德建,江龙.一般时间区间L^p-半鞅序列的单调极限定理[J].数学年刊A辑,2019,40(2):211~230 |
| 一般时间区间L^p-半鞅序列的单调极限定理 |
| Monotonic Limit Theorem for Lp-Semimartingales on General Time Horizon |
| Received:March 12, 2016 Revised:March 20, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0017 |
| 中文关键词: Monotonic limit theorem, Penalization method,Weak convergence,Nonlinear Doob-Meyer decomposition, Backward stochastic differential equation |
| 英文关键词:Monotonic limit theorem, Penalization method,Weak convergence,Nonlinear Doob-Meyer decomposition, Backward stochastic differential equation |
| 基金项目: |
| Author Name | Affiliation | E-mail | | SHI Xuejun | School of Mathematics and Statistics, Shandong NormalUniversity, Jinan 250014, China. | shixuejun216@126.com | | FENG Qun | School of Business, University of Jinan, Jinan 250002, China. | smfengq@ujn.edu.cn | | TIAN
Dejian | School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China. | tiandejian1985@163.com | | JIANG Long | Corresponding author. School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China. | smfengq@ujn.edu.cn |
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| 中文摘要: |
| 基于倒向随机微分方程(BSDE)
和非线性期望理论中惩罚方法的启发, 研究并得到了一般时间区间上
$L^p${-}半鞅序列的单调极限定理. 该结果的证明并非经典结果的平凡推广, 新的框架让我们面对许多新问题,
它将在一般框架下
$g${-}上鞅的Doob-Meyer型分解以及受限BSDE解的存在性等问题的探索中发挥重要作用. |
| 英文摘要: |
| In this paper, a new version of monotonic
limit theorem is established for a sequence of $L^p$-semimartingales
on general time interval, motivated by the penalization method in
the theories of backward stochastic differential equations (BSDEs for short)
and nonlinear expectations. It is just the general framework
that makes us have to tackle many new problems. And also this
non-trivial result plays a key role in exploring the more general
form of nonlinear Doob-Meyer Decomposition of $g$-supermartingale
and the existence of solutions to BSDEs with constraints. |
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