Q过程构造论中的H-条件

H-Condition In the Construction Theory of Q-Processes

设E为可列集,Q为E×E上全稳定Q-矩阵,在[1]中,侯振挺教授得到“Q过程的唯一性准则”,这个准则的核心是给出了如下条件: ??(1) 其中φ(λ)=(φij(λ),i,j∈E,λ>0)为最小Q过程. 我们称(1)为H-条件.我们发现H-条件在Q过程构造论中起重要的作用.本文就H-条件在Q过程定性理论及瞬时态Q过程构造论中的作用进行一些讨论.

Let E be a countable set, Q be a totally stable Q-matrix in E x E.In, Prof.Hou Zhenting obtained 'the criteria for the unique-ness of Q-processes'.The crux of this criteria is the following conditioin ?? where φ(λ) = (φ_(ij)(λ), i, j∈E, λ>0) is a minimal Q-process.We call (2) H-condition.It plays an important role in the construction theory of Q-processes.In this paper, We simply discuss the application of H-condition in the qualitative theory of Q-processes and the construction theory of Q-processes of the instantaneous state.