| 无穷水平跳扩散正－倒向随机微分方程的解与比较定理 |
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| 引用本文： | 尹居良,司徒荣.无穷水平跳扩散正－倒向随机微分方程的解与比较定理[J].中山大学学报(自然科学版),2008,47(1):5-8,12. |
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| 作者姓名： | 尹居良 司徒荣 |
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| 作者单位： | 1. 暨南大学统计学系,广东,广州,510630
2. 中山大学数学系,广东,广州,510275 |
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| 摘 要： | 研究了无穷水平跳扩散正—倒向随机微分方程解的存在唯一性以及比较定理。首先，在非李氏系数和弱单调性条件下，运用平滑技术，证明了无穷水平跳扩散正-倒向随机微分方程适应解的存在唯一性。在此基础上，利用停时技术和广义Tanaka公式，证明了上述方程适应解的比较定理。
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| 关 键 词： | 跳扩散正—倒向随机微分方程 适应解 比较定理 Tanaka公式 |
| 文章编号： | 0529-6579（2008）01-0005-05 |
| 收稿时间： | 2007-05-29 |
| 修稿时间： | 2007年5月29日 |
On Solutions and Comparison Theorems of Infinite Horizon Forward-Backward Stochastic Differential Equations with Poisson Jumps |
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| YIN Ju-liang,SITU Rong.On Solutions and Comparison Theorems of Infinite Horizon Forward-Backward Stochastic Differential Equations with Poisson Jumps[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2008,47(1):5-8,12. |
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| Authors: | YIN Ju-liang SITU Rong |
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| Institution: | 1.Department of Statistics, Jinan University, Guangzhou 510630, China 2. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China |
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| Abstract: | Existence and uniqueness and comparison theorems of solutions to infinite horizon forward-backward stochastic differential equations with Poisson jumps (FBSDEs) are discussed. Firstly, the existence and uniqueness of adapted solutions to such FBSDEs is proved by applying smoothing technique under assumptions of non-Lipschitz conditions and weak monotonicity on the coefficients. Then two comparison theorems for such FBSDEs are derived by using stopping time method and the Tanaka formula. |
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| Keywords: | forward-backward stochastic differential equations with Poisson jumps adapted solution comparison theorem Tanaka formula |
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