Linear birth and death processes with killing

Abstract

We analyze a class of linear birth and death processes X(t) with killing. The generator is of the form λ _i = bi + θ, µ_i = ai, γ _i = ci, where γ _i is the killing rate. Then P{killed in (t, t + h) | X(t) = i} = γ _ih + o(h), h ↓ 0. A variety of explicit results are found, and an example from population genetics is given.