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| Boundary Value Problems for First Order Stochastic Differential Equations | |
| 引用本文： | 王妍 韩月才. Boundary Value Problems for First Order Stochastic Differential Equations[J]. 东北数学, 2007, 23(6): 541-548 |
| 作者姓名： | 王妍 韩月才 |
| 作者单位： | [1]Institute of Mathematics, Jilin University, Changchun, 130012 [2]School of Mathematics, Jilin University, Changchun, 130012;School of Mathematics and System Science, Shandong University, Jinan, 250100 |
| 基金项目： | Acknowledgments The authors express their sincere thanks to Prof. Li Yong for his instructions and encouragement. |
| 摘 要： | In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example. |
| 关 键 词： | 一阶随机微分方程 边值问题 数学分析 理论研究 |
| 文章编号： | 1000-1778（2007）06-0541-08 |
| 收稿时间： | 2007-05-31 |
| 修稿时间： | 2007-05-31 |
Boundary Value Problems for First Order Stochastic Differential Equations |
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| WANG Yan HAN Yue-cai. Boundary Value Problems for First Order Stochastic Differential Equations[J]. Northeastern Mathematical Journal, 2007, 23(6): 541-548 | |
| Authors: | WANG Yan HAN Yue-cai |
| Affiliation: | Institute of Mathematics, Jilin University, Changchun, 130012;School of Mathematics, Jilin University, Changchun, 130012; School of Mathematics and System Science, Shandong University, Jinan, 250100 |
| Abstract: | In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition (in the sense of expectation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example. |
| Keywords: | stochastic differential equation boundary value problem contractionmapping principle Leray-Schauder fixed point theorem |
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