7 A doubly stochastic Poisson process is an inhomogenous Poisson process in which the rate function (t ) is itself a random process Show that the simple birth process with birth rate is a doubly stochastic Poisson process N for which (t ) Nt

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Question: 7. A doubly stochastic Poisson process is an inhomogenous Poisson process in which the rate function (t ) is itself a random process. Show that

7. A ‘doubly stochastic’ Poisson process is an inhomogenous Poisson process in which the rate function λ(t ) is itself a random process. Show that the simple birth process with birth rate λ is a doubly stochastic Poisson process N for which λ(t ) = λNt .

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