含瞬时态、具有突变率的广义生-灭Q-矩阵(Ⅱ)  

AN EXTENDED BIRTH-DEATH Q-MATRIX WITH INSTANTANEOUS STATE AND CATASTROPHES (Ⅱ)

作　　者：吴群英[1] 张汉君[2] 侯振挺[2] 

机构地区：[1]桂林工学院数理系,广西桂林541004 [2]中南大学数学学院,长沙410075

出　　处：《数学年刊（A辑）》2003年第5期555-564,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19871006);广西自然科学基金(No.桂科基0339071)

摘　　要：研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。A new structure with the special property that instantaneous state and catastrophes is imposed to ordinary birth-death processes is considered. Under the condition that the underlying birth-death process is non-zero-exit, the authors are able to give easy-checking existence criteria for such Markov processes. All the Q-processes and all the honest Q-processes are explicitly constructed. Recurrent and ergodicity properties for the honest Q-processes are investigated. Surprisingly, it can be proved that all the honest Q-processes are ergodicity without necessarily imposing any extra conditions. Ergodicity of such processes is also investigated and solved. Equilibrium distributions are established. The condition that the honest Q-processes is symmetric is given. Two examples are provided to illustrate our results.

关 键 词：瞬时态 广义生-灭Q过程 构造定理 存在性 遍历性 

分 类 号：O151.21[理学—数学]