In the diffusion approximation to a branching process with immigration, we set (t, x)=()x+ and 2(t, x)=(+)x+, where and are the birth and

In the diffusion approximation to a branching process with immigration, we set µ(t, x)=(α−ν)x+η and σ2(t, x)=(α+ν)x+η, where α

and ν are the birth and death rates per particle and η is the immigration rate. Justify these expressions by appealing to a continuous-time Markov chain.