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

83. 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

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)

Transcribed Image Text:

m(t) = X(s) ds Jo