I have this as part of a theorem for the sum of two poisson processes being itself a poisson process. I don't particularly understand why the fourth line equals the last line of the theorem. I believe there should be a λµh^2 in the last line but believe this has been swallowed into the o(h) part of the last line. Why is it the case that this term can disappear please? Thanks
Let Zt = Xt + Yt
P[Zt+h − Zt = 0] = P[Xt+h − Xt = 0, Yt+h − Yt = 0]
= P[Xt+h − Xt = 0]P[Yt+h − Yt = 0]
= (1 − λh + o(h))(1 − µh + o(h))
= 1 − (λ + µ)h + o(h), as h ↓ 0