双无限环境中马氏链的常返和暂留性  

THE RECCURRENCE AND TRANSIENCE FOR MARKOV CHAINS IN DOUBLE INFINITE ENVIRONMENTS

作　　者：汪和松[1,2] 李应求[2] 王众[2] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081 [2]长沙理工大学数学与计算科学学院,长沙410076

出　　处：《系统科学与数学》2009年第3期418-424,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10771021;10471012);教育部留学回国人员科研启动基金([2005]564);湖南省教育厅(07A003;06C099)资助项目.

摘　　要：证明了常返和暂留是一对互斥概念,如果(?)是π-不可约的且π是平稳的,则各种常返、暂留概念是等价的,讨论了暂留与非本质的等价性问题.The incompatibility between the concept of the reccurrence and that of the transience is proved. Furthermore, if X^→ is π-irreducible and π is stationary, various concepts of the reeeurrence and that of the transience are equivalent respectively. In addition, equivalence between transience and inessential sets is discussed.

关 键 词：双无限随机环境 马氏链 π-不可约 常返 暂留 

分 类 号：O211.62[理学—概率论与数理统计] O174.13[理学—数学]