一个带反馈的随机系统

ON URN MODEL WITH THE FEEDBACK

本文提出并研究了一个带反馈的随机系统。证明了描述此系统的随机过程{X_n,n≥0}是齐次非周期常返的不可约的强Markov链。指出它既不是独立增量过程也不是鞅。求出了它的转移矩阵和终极分布。

In this paper,We have presented a model of the urn with the feedback and have established its probability model.We have proved: i){x_n,n≥O}—discussed object,is the homogeneous,recurrent, noncyclic and incommensurable strong markov chains. ii)But it is neither martingales nor independent increment process. Finally we point out the generalizations and applications of the model.