论文标题
在分支扩散引起的一类非线性微分方程上
On a Class of Non-linear Differential Equations Arising from Branching Diffusions
论文作者
论文摘要
考虑了由称为分支布朗运动的随机过程产生的非线性微分方程。我们找到了一个明确的解决方案，并使用概率思想在某些有界条件下显示了解决方案的独特性。我们讨论非负解决方案。我们还将这一想法推广到一类非线性抛物线微分方程，我们称之为概率抛物线方程。
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using probabilistic ideas. We discuss non-negative solutions. We also generalize this idea to a class of non-linear parabolic differential equations which we call probabilistic parabolic equations.
