Suppose that {N0(t), t 0} is a Poisson process with rate = 1. Let (t) denote

Suppose that {N0(t), t 0} is a Poisson process with rate λ = 1. Let λ(t) denote a nonnegative function of t, and let m(t) =

t 0

λ(s) ds Define N(t) by N(t) = N0(m(t))

Argue that {N(t), t 0} is a nonhomogeneous Poisson process with intensity function λ(t), t 0.

Hint: Make use of the identity m(t + h) − m(t) = m

(t)h + o(h)