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| SINGLE BIRTH PROCESSES |
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Citation： |
CHEN Mufa.SINGLE BIRTH PROCESSES[J].Chinese Annals of Mathematics B,1999,20(1):77~82 |
| Page view： 1084
Net amount： 709 |
Authors： |
CHEN Mufa; |
Foundation： |
the National Natural Science Foundation of China, Qiu Shi Science& Technology Foundation, DPFIHE and Mathematical Center of the Ministry of Education of China |
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| Abstract： |
The single birth process is a Markov chain,
either time-continuous or time-discrete, valued in the
non-negative integers: the system jumps with positive rate
from $k$ to $k+1$ but not to $k+j$ for all $j\ge 2$ (this explains the meaning of ``single birth'').
However, there is no restriction for the jumps from $k$ to
$k-j\,(1\le j\le k)$. This note mainly deals with the uniqueness problem for the time-continuous processes with an extension: the jumps from $k$ to $k+1$ may also be forbidden for at most finite number of $k$. In both cases (time-continuous or -discrete), the hitting probability and the
first moment of the hitting time are also studied. |
Keywords： |
Markov chains, Single birth process, Uniqueness criterion |
Classification： |
60J27, 60J25 |
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