| 完全耦合的正倒向随机微分方程及相应的偏微分方程系统 |
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| 引用本文： | 吴臻,于志勇. 完全耦合的正倒向随机微分方程及相应的偏微分方程系统[J]. 数学年刊A辑(中文版), 2004, 0(4) |
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| 作者姓名： | 吴臻 于志勇 |
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| 作者单位： | 山东大学数学与系统科学学院，山东大学数学与系统科学学院 济南 250100，济南 250100 |
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| 基金项目： | 国家自然科学基金(No.10371067)，教育部优秀青年教师资助计划，霍英东青年教师基金，博士点基金，山东省优秀中青年科学家科研奖励基金 |
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| 摘 要： | 本文利用完全耦合的正倒向随机微分方程,对一类耦合了一个代数方程的二阶拟线性抛物型偏微分方程系统,给出概率表示。在适当的假设下,得到这类偏微分方程系统粘性解的存在唯一性结果。
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| 关 键 词： | 正倒向随机微分方程 抛物型偏微分方程 比较定理 粘性解 |
FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED PARTIAL DIFFERENTIAL EQUATIONS SYSTEM |
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| WU Zhen YU Zhiyong. FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED PARTIAL DIFFERENTIAL EQUATIONS SYSTEM[J]. Chinese Annals of Mathematics, 2004, 0(4) |
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| Authors: | WU Zhen YU Zhiyong |
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| Abstract: | This paper gives the probabilistic interpretation for one system of the second order quasilinear parabolic partial differential equations combined with an algebra equation using fully coupled forward-backward stochastic differential equation. The existence and uniqueness result of the viscosity solution for this kind of partial differential equations systems under the milder hypothesis was obtained. |
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| Keywords: | Forward-backward stochastic differential equation Parabolic partial differential equation Comparison theorem Viscosity solution |
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