一类三阶双随机矩阵的嵌入问题

The Embedding Problem for a Class of Three-order Bistochastic Matrix

齐次马氏链的嵌入问题可陈述如下:“任给一个随机矩阵P=(pij,i、j∈E)(E 为可列集),求转移矩阵P(t)(t≥0) ,使P(1) =P”.若这样的P(t)存在,则称P 为一个离散骨架,而P(t)为P 的一个连续扩充.进而,若P(t)的密度矩阵Q 是“双保守”的,即Q 的行和与列和均为0,则称离散骨架为双随机型的,本文在E 仅含有三个元素的情形下,给出了双随机型离散骨架的判定准则。

The embedding problem for the Maruov chains can be stated asfollowing:“Given an arbitrary stochastic matrix P=(p_(ii),i、j∈E)(E is a denumerable set),find transition function P(t)(t≥0)such that P(1) =P”.If such a P(t)exists,then P is called a di-screte skeleton and the P(t)a coutinuous expansion of P.Furth-eremore,if the intensity matrix Q is of bicouservative type,i.e.the sums of the rows and columns are both equal to one,thenwe name the discrete skeleton of P(t)to be of bistochastic type.In this paper the criteria of discrete skeleton of bistochastic typeare given,where the set E has only three elements.