| 超布朗运动与无界区域上一类非线性微分方程 |
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| 引用本文： | 任艳霞,吴荣,杨春鹏. 超布朗运动与无界区域上一类非线性微分方程[J]. 数学学报, 1999, 42(1): 105-110. DOI: cnki:ISSN:0583-1431.0.1999-01-016 |
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| 作者姓名： | 任艳霞 吴荣 杨春鹏 |
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| 作者单位： | 1. 南开大学数学系,天津,300071
2. 郑州大学数学系,郑州,450052 |
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| 基金项目： | 国家自然科学基金，博士点基金 |
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| 摘 要： | 本文得到了超布朗运动的一个极限定理，并用超布朗运动给出了区域D上非线性微分方程的Dirichlet问题与随机Dirichlet问题非负有界解的精确表达式．
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| 关 键 词： | 超布朗运动 非线性微分方程 Dirichlet问题 随机Dirichlet问题 |
| 修稿时间： | :1997-05-3 |
Super-Brownian Motion and One Class of Nonlinear Differential Equations on Unbounded Domains |
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| Ren Yanxia,Wu Rong,Yang Chunpeng. Super-Brownian Motion and One Class of Nonlinear Differential Equations on Unbounded Domains[J]. Acta Mathematica Sinica, 1999, 42(1): 105-110. DOI: cnki:ISSN:0583-1431.0.1999-01-016 |
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| Authors: | Ren Yanxia Wu Rong Yang Chunpeng |
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| Affiliation: | Ren Yanxia Wu Rong;(Department of Mathematics, NankaiUniversity, Tianjin 300071, P. R. China);Yang Chunpeng;(Department of Mathematics, ZhengzhouUniversity, Zhengzhou 450052, P. R. China) |
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| Abstract: | Let where a(x) and γ(x) are positive bounded integrable functions in D and We first establish a limit theorem of the super-Brownian motion X with parameters Then in Section 3 and 4, we study the structure of the set of all positive bounded solutions of the differential equation in a domain D (bounded or unbounded). All positive bounded solutions with Dirichlet boundary condition or stochastic Dirichlet boundary condition are represented in terms of the super-Brownian motion X. |
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| Keywords: | Super-Brownian motion Nonlinear differential equation Dirichlet problem Stochastic Dirichlet problem |
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