摘要
首先简要介绍自1977年左右开始的寻找连续时间马尔可夫跳过程实用的唯一性充分条件的故事.对于一般状态空间的一般性结果是1985年得到的.为展示这些充分条件的精确性,于1991年找到非唯一性的对偶判别准则.本文主要限于离散空间(此时的跳过程也称为Q过程或马尔可夫链).在这种情况下,我们将在文末证明上述充分条件也是必要的.我们还将举例说明不论对于唯一性或非唯一性,我们的充分条件不仅强有力,而且精确.
The note begins with a short story on seeking for a practical sufficiency theorem for the uniqueness of time-continuons Markov jump processes, starting around 1977. The general result was obtained in 1985 for the processes with general state spaces. To see the sufficient conditions are sharp, a dual criterion for non-uniqueness was obtained in 1991. This note is restricted however to the discrete state space （then the processes are called Q-processes or Markov chains）, for which the sufficient conditions just mentioned are showing at the end of the note to be necessary. Some examples are included to illustrate that the sufficient conditions either for uniqueness or for non- uniqueness are not only powerful but also sharp.
出处
《应用概率统计》
CSCD
北大核心
2015年第2期213-224,共12页
Chinese Journal of Applied Probability and Statistics
基金
supported in part by the National Natural Science Foundation of China(11131003)
the"985"project from the Ministry of Education in China
the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
