论文标题
与移民进行随机分支。 Lyapunov稳定性
Branching Random Walks with Immigration. Lyapunov Stability
论文作者
论文摘要
我们考虑在具有移民和无限数量初始颗粒数量的多维晶格上进行连续的对称分支随机行走。我们假设在每个晶格点，颗粒的生育和死亡过程都由Bienayme-Galton-Watson分支过程描述。颗粒移民的假设是，新粒子可以从外部出现在每个晶格点。研究的主题是晶格上粒子场的极限分布。在晶格上的固定点处，在任意时间矩时粒子数的相关函数的微分方程将得到。我们研究了该过程的每个晶格点和Lyapunov的稳定性的前两个矩的渐近行为。在假设出生，死亡和移民强度取决于晶格点的假设下，考虑到Lyapunov的稳定性。
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is described by a Bienayme-Galton- Watson branching process. The assumption on immigration of particles is that a new particle can appear at every lattice point from the outside. The subject of the study is a limit distribution of the particle field on the lattice. The differential equations for correlation functions for the number of particles at an arbitrary time moment at the fixed points on the lattice are obtained. We study the asymptotic behaviour for the first two moments of a number of particles at every lattice point and Lyapunov stability of the process. The Lyapunov stability is considered under the assumptions that birth, death and immigration intensities depend on the lattice points.
