Question: Suppose that (No(), 0) is a Poisson process with rate = 1. Let (1) denote a nonnegative function of t, and let Define N(t) by

Suppose that (No(), 0) is a Poisson process with rate = 1.

Let (1) denote a nonnegative function of t, and let Define N(t) by m(t)=2(s) ds N(t) = No(m(t)) Argue that [N(t), t 0) is a nonhomogeneous Poisson process with intensity function A(1), 0.

Hint: Make use of the identity m(t + h) m(t) = m'(t)h + o(h)

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