依时变化的随机环境中的分枝随机游动的局部极限定理的二阶展开

A Second Order Correction of the Local Limit Theorem for a Branching Random Walk with a Random Environment in Time on Z

考虑了Z^(d)中随机环境中的分枝随机游动,其中分枝机制和粒子迁移的分布律均依时间变化.对任意给定点z∈Z^(d),令Z;(z)表示位于该点处的n代粒子的个数.给出了Z_(n)(z)的二阶渐近展开表达式.

Consider a branching random walk on Z^(d) with a random environment in time,where the branching offspring distribution and the migration law change as times goes by.Under the mild moment conditions,we derive the second order expansion for Z_(n)(z),which counts the number of particles of generation n at z ∈ Z^(d).