Approximation of the invariant probability measure of an infinite stochastic matrix
Approximation of the invariant probability measure of an infinite stochastic matrix
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无限随机矩阵的不变概率测度的近似
DOI：
10.2307/1426428
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发表时间：
1980
影响因子：
1.2
通讯作者：
D. Wolf
中科院分区：
文献类型：
--
作者：
D. Wolf
令 P 表示具有唯一不变概率测度 π 的不可约正循环无限随机矩阵。我们考虑收敛到 P（逐点）的随机矩阵的序列 {P m }m∊N，使得每个 Pm 至少有一个不变的概率测度 π m 。本文的目的是找到确保至少一个序列 {π m }m∊N 收敛于 π （逐点）的条件。这包括 P m 是有限矩阵的情况，这是特别令人感兴趣的。结果表明，存在一个有限随机矩阵序列，可以很容易地构造该序列，使得{π m }m∊N 收敛于π。一般情况下给出的条件与福斯特的病情密切相关。
Let P denote an irreducible positive recurrent infinite stochastic matrix with the unique invariant probability measure π. We consider sequences {P m }m∊N of stochastic matrices converging to P (pointwise), such that every Pm has at least one invariant probability measure π m . The aim of this paper is to find conditions, which assure that at least one of sequences {π m }m∊N converges to π (pointwise). This includes the case where the P m are finite matrices, which is of special interest. It is shown that there is a sequence of finite stochastic matrices, which can easily be constructed, such that {π m }m∊N converges to π. The conditions given for the general case are closely related to Foster's condition.