Solution
= Solution
With $p_{-1}=0$, the <birth-death master equation> for birth rate $b_n=Bn$ and death rate $d_n=Dn$ is
$$
\dot p_n=B(n-1)p_{n-1}+D(n+1)p_{n+1}-(B+D)np_n,
\qquad n\geq0.
$$
= Solution
With $p_{-1}=0$, the <birth-death master equation> for birth rate $b_n=Bn$ and death rate $d_n=Dn$ is
$$
\dot p_n=B(n-1)p_{n-1}+D(n+1)p_{n+1}-(B+D)np_n,
\qquad n\geq0.
$$