具有吸收态单生过程以概率1灭绝的充分必要条件  

A sufficient and Necessary Condition for the Probability of Extinction to Equal one of Single - birth Process with Absorbing State

作　　者：艾俊勇[1] 刘源远[2] 蒋勇辉 

机构地区：[1]邵阳学院数学系,湖南邵阳422000 [2]中南大学数学学院,湖南长沙410075 [3]长沙县第一中学星沙校区,湖南长沙410100

出　　处：《邵阳学院学报（自然科学版）》2004年第4期20-21,共2页Journal of Shaoyang University：Natural Science Edition

摘　　要：设Q为正则单生Q-矩阵,其Q-过程记为fif(t),将Q中第一行所有元素改为0,即q0j=0,j∈E,得到含吸收态"0"的正则Q-矩阵Q,其相应的Q-过程记为fij(t).我们运用分析的办法得到了具有吸收态的单生过程fij(t)以概率1灭绝的充分必要条件是fij(t)常返.Let Q be a regular single-birth Q-matrix and fij(t) be the corresponding Q-Process. Changing all the elements in the firstrow of Q into 0,that is, qoj= 0,j ∈ E, we get a regular Q-matrix Q with an absorbing state'0' and denote by fok(t) the corresPonding Q-Process. With analytic method we get that the probability of extinction of the process fij(t) equals one if and only if the original process fij(t) is recurrent

关 键 词：Q-过程 单生过程 灭绝概率 

分 类 号：O211.62[理学—概率论与数理统计]