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