49. Suppose that {0(), / > 0} is a Poisson process with rate A = 1 ....

49. Suppose that {ËÔ0(ß), / > 0} is a Poisson process with rate A = 1 .

Let ë(ß) denote a nonnegative function of and let m(x)

÷ < t F(x) = m(t) '

÷ > t Define N(t) by N0(m(t))

Argue that [N(t)9 t > 0} is a nonhomogeneous Poisson process with intensity function ë(ß), t > 0.
Hint: Make use of the identity m{t + h) - m(t) = m'(t)h + o(h)