测度值分枝马氏过程及相关Fisher-KPP方程性质研究

本项目要研究测度值分枝马氏过程及其对应的非线性微分方程方程，其中测度值分枝马氏过程主要包括分枝马氏过程与超过程，涉及的非线性偏微分方程是Fisher-KPP方程。我们计划研究上临界测度值分枝马氏过程的各种极限收敛速度；下临界测度值分枝马氏过程的拟稳定分布及条件过程极限性质；随机环境中分枝粒子系统最右端粒子的极限性质及相应Fisher-KPP方程的行波解及解的极限性质。

In this project we will investigate measure-valued branching Markov processes and related nonlinear differential equations, including branching Markov processes and superprocesses, where the related nonlinear differential equations is Fisher-KPP equation. We plan to investigate various kinds of convergence rates for supercritical measure-valued branching Markov processes, quasi-stationary distributions and limit properties of conditioned processes for supercritical measure-valued branching Markov processes; the limit behavior of the right most position of branching particle systems and the traveling wave solutions and limit properties of solutions of the related Fisher-KPP equations in random environments.