| 具有Osgood型生成元的多维倒向重随机微分方程 |
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| 引用本文： | 王先飞,江龙,马娇娇. 具有Osgood型生成元的多维倒向重随机微分方程[J]. 山东大学学报(理学版), 2015, 50(8): 24-33. DOI: 10.6040/j.issn.1671-9352.0.2015.038 |
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| 作者姓名： | 王先飞 江龙 马娇娇 |
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| 作者单位： | 中国矿业大学理学院, 江苏 徐州 221116 |
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| 基金项目： | 国家自然科学基金资助项目(11371362) |
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| 摘 要： | 研究了一类多维倒向重随机微分方程, 其生成元f关于y满足Osgood条件,且生成元g关于y满足一类新的非Lipschitz条件. 建立了该类方程的一个解的存在唯一性定理和一个稳定性定理,并给出了该类方程在一维情形下解的比较定理.
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| 关 键 词： | Osgood条件 稳定性定理 比较定理 存在唯一性定理 倒向重随机微分方程 |
| 收稿时间： | 2015-01-09 |
Multidimensional backward doubly stochastic differential equations with generators of Osgood type |
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| WANG Xian-fei,JIANG Long,MA Jiao-jiao. Multidimensional backward doubly stochastic differential equations with generators of Osgood type[J]. Journal of Shandong University, 2015, 50(8): 24-33. DOI: 10.6040/j.issn.1671-9352.0.2015.038 |
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| Authors: | WANG Xian-fei JIANG Long MA Jiao-jiao |
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| Affiliation: | College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China |
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| Abstract: | A class of multidimensional backward doubly stochastic differential equations whose generator f satisfies the Osgood condition in y and generator g satisfies non-Lipschitz condition in y was studied. An existence and uniqueness theorem and a stability theorem of solutions for this kind of equations were established, and a comparison theorem for solution of the class of one-dimensional situation was proposed. |
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| Keywords: | backward doubly stochastic differential equations Osgood condition existence and uniqueness theorem stability theorem comparison theorem |
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