超布朗运动与无界区域上一类非线性微分方程  

Super-Brownian Motion and One Class of Nonlinear Differential Equations on Unbounded Domains

作　　者：任艳霞[1] 吴荣[1] 杨春鹏[2] 

机构地区：[1]南开大学数学系,天津300071 [2]郑州大学数学系,郑州450052

出　　处：《数学学报（中文版）》1999年第1期105-110,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;博士点基金

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．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.

关 键 词：超布朗运动 非线性微分方程 极限定理 无界区域 

分 类 号：O211.6[理学—概率论与数理统计] O175[理学—数学]