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

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.