Ӧ�ø���ͳ�� 2015, 31(2) 213-224 DOI:      ISSN: 1001-4268 CN: 31-1256

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��Ψһ�Գ�������Ĺ���. ����һ��״̬�ռ��һ���Խ����1985��õ���.
Ϊչʾ��Щ��������ľ�ȷ��, ��1991���ҵ���Ψһ�ԵĶ�ż�б�׼��.
������Ҫ������ɢ�ռ�(��ʱ��������Ҳ��ΪQ���̻�����ɷ���). �����������,
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�ؼ����� �б�׼��   Ψһ��   ����ɷ���   ����ɷ�������.  
Practical Criterion for Uniqueness of Q-Processes
Chen Mufa
School of Mathematical Sciences, Beijing Normal University; Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education
Abstract:

The note begins with a short story on seeking for a practical
sufficiency theorem for the uniqueness of time-continuous 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.

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