Question: Exercise 11.3 If N is a Poisson process with rate , show that P(Nt+h = 0) = 1 h + o(h) P(Nt

Exercise 11.3 If N is a Poisson process with rate λ, show that P(Nt+h = 0) =



1 − λh + o(h)



P(Nt = 0)

for small positive values of h. Hence, show that p(t) = P(Nt = 0) satisfies the differential equation p′(t) = −λp(t ).

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