带形上分枝随机游动中λ→(x,n)的均值

THE EXPECTATION OF λ→(x,n) FOR A BRANCHING RANDOM WALK ON A STRIP

考虑带形上的分枝随机游动,假定每代粒子均以相同的概率分布独立产生后代的同时,每个粒子又以带形上的随机游动运动.通过合理构造变量和递推归纳的方法,得到了时间n位于第x列的粒子数λ→(x,n)的均值.

Consider a model of branching random walk on a strip, where the particles reproduce in a Galton-Watson process with a fixed reproduction law, but move as a random walk on a strip. By the method of recursion, we obtain the expectation of →/λ（x,n）which is the number of particles located in layer x at time n.