三阶有势 Markov 过程的离散骨架

THE CR1TERIA OF DISCRETE SKELETON OF 3-ORDER POTENTIAL MARKOV PROCESSES

本文是关于三阶嵌入问题的一系列研究的一个阶段性结果,讨论三阶有势 Markov过程的离散骨架的判定问题:在§2中我们首次对三阶 Q-矩阵及其对应的 Q-过程和离散骨架进行分类并得到各类三阶离散骨架的表现定理,从而对全部三阶离散骨架作出了十分细致的完整的刻划,这一表现定理实际上已为一般三阶嵌入问题的彻底解决奠定了基础,在§3中我们给出了各类三阶有势 Markov 过程的离散骨架的判定准则,从而使这一特殊类型的离散骨架的判定问题彻底解决。

In thhis parper the embedding problem for three order potential Markovprocesses is discussed.In §2 the classification of 3-order Q-matrices as well asits Q-processes and discrete skeletons is given for the first time and the repre-sentation theorem whcih completely describes all 3-order discrete skeletons isabtained.In §3 the criterias of discrete skeleton of 3-order potential Markovprocesses are prooved.