【摘要】 <正> 设E是一至多可列集,P=(P_ij)是E上的随机矩阵(即对一切i,j∈E,P_ij≥0,sum form K∈E （Pik）=1)。以下称状态空间是E,转移概率矩阵是P的任何齐次马尔可夫链（x_n,n≥0）（所在的概率空间是（Ω,F,IP））为P链。仿[1]有: 定义:称E上随机矩阵P具有重合性质,如果对任何i,j∈E及任何概率空间(Ω,更多还原

【Abstract】 Let E be a almost countable set, and P = (pij, i, j∈ E) be a stochastic matrix. Any Markov Chain (xn, n≥O) with transition matrix P is Called a P-Chain.Definition. A stochastic matrix P is said to have coincidence property (abbrev. c. p.), if:Where (xn, n≥0), (yn, n≥0) are arbitrary mutually independent P-chains on (Ω, F, IP), i, j∈E.When does P have c. p. ? In this paper, the following results are Obtained.Theorem A. Suppose that. P is irreducible, its period is 1, and there exists i∈E such that Then P has c. p. Theorem B: Let E={0,1,2,…}and P satisfies the following conditions:Then, the matrix P has c. p. Theorem C. Suppose that.E = {(z1,z2,…,zm): Z1, z2, …, zm are integers} P =(pxy, x,y∈E) satisfies: pxy = po y-x for all x,y∈ E. A necessary and sufficient condition for p to have c. p. is the following:Where (u,x) be inner product.Certain more general conditions sufficient for c. p. are obtained, several examples are given.更多还原