On Total Progeny of Multitype Galton-Watson Process and the First Passage Time of Random Walk on Lattice  

作　　者：Hua Ming WANG 

机构地区：[1]Department of Mathematics,Anhui Normal University

出　　处：《Acta Mathematica Sinica,English Series》2014年第12期2161-2172,共12页数学学报（英文版）

基　　金：Supported by National Nature Science Foundation of China(Grant No.11226199)

摘　　要：In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and（2-1） random walk.Consequently,we could give the probability generating functions and the distributions of the first passage time of corresponding random walks.Especially,for recurrent random walk which could stay at its position with probability 0 〈 r 〈 1,we show that the tail probability of the first passage time decays as 2/√π（1-r）1/√n= when n →∞.In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and（2-1） random walk.Consequently,we could give the probability generating functions and the distributions of the first passage time of corresponding random walks.Especially,for recurrent random walk which could stay at its position with probability 0 〈 r 〈 1,we show that the tail probability of the first passage time decays as 2/√π（1-r）1/√n= when n →∞.

关 键 词：Multitype branching process total progeny random walk 

分 类 号：O153.1[理学—数学]