Birth-death master equation
= Birth-death master equation
For birth rates $b_n$, death rates $d_n$, and state probabilities $P_n$,
$$
\dot P_n=b_{n-1}P_{n-1}+d_{n+1}P_{n+1}-(b_n+d_n)P_n.
$$
= Birth-death master equation
For birth rates $b_n$, death rates $d_n$, and state probabilities $P_n$,
$$
\dot P_n=b_{n-1}P_{n-1}+d_{n+1}P_{n+1}-(b_n+d_n)P_n.
$$