多元马氏链的状态分类及其基本性质

基金项目:

国家自然科学基金项目（71372154）不完备生产条件下多工厂柔性JIT生产-库存优化与原料供给系统研究

详细信息

The Classification of State for Multivariate Markov Chain and It’s Basic Properties

摘要: 基于高维马氏模型,结合传统马氏链状态的基本概念,提出了多元马氏模型的可达性、互通性、首达时间和概率等新定义.在此基础上,给出了多元马氏模型的常返性、遍历性和周期性等概念.在对其状态进行分类的同时,提出了多元马氏模型下的切普曼-柯尔莫哥洛夫方程,并利用该方程研究了状态之间的关系.结论表明，在互通的状态下,状态间的关系具有对称性、传递性、同返性和同周期性等属性.
- 多元马氏链 /
- 状态分类 /
- 基本性质
Abstract: Based on high-dimensional Markovian model and combining the basic conception of states for traditional Markov chain, the new definitions of accessibility, interoperability, first arrival time and its probability for multivariate Markovian model are defined, and the notion of recurrence, ergodicity and periodicity are given by these definitions, too. Moreover, the Chapman-Kolmogorov equation of multivariate Markovian model is proposed, and using this equation study on basic property of relationships among the states. The conclusion show that there are symmetry, transitivity, identical recurrence and period in relationships among states under interoperable state condition.
- Multivariate Markov chain /
- classification of state /
- basic properties

1.	刘婧怡，蒋雅萌，冯伟，郑凤，许新华. 自愈合离子凝胶的制备及传感测试. 大学化学. 2022(05): 304-310 . 百度学术
2.	郭媛媛，蒋洪伟，袁冬，唐彪，周国富. 电润湿显示材料与器件技术研究进展. 液晶与显示. 2022(08): 925-941 . 百度学术
3.	刘丽明，闫航瑞. 氯化钠液滴在特氟龙表面润湿行为的电控调节研究. 传感器与微系统. 2021(02): 38-40+43 . 百度学术