Stochastic solutions to evolution equations of non-local branching processes
Nonlinear Analysis(2020)
摘要
We give a probabilistic representation for the solution to a nonlinear evolution equation induced by a measure-valued branching process. We first construct the involved branching processes on the set of all finite configurations of a given set, with a killing rate induced by a continuous additive functional, and with a non-local branching procedure given by a sequence of Markovian kernels. The main application is to prove stochastic aspects for a nonlinear evolution equation related to the Neumann problem and the surface measure on the boundary, which corresponds to the reflecting Brownian motion as base movement, taking the killing rate given by the local time on the boundary. We use specific potential theoretical tools.
更多查看译文
关键词
60J80,35J60,60J68,60J45,60J35,47D07
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要