A property of the expected value of a Poisson Process

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Let X(t) be a Poisson Process and $f\geq0$. Show that $E[e^{-\sum_{n=1}^{\infty}f(W_n)}]=e^{-\lambda \int_0^\infty(1-e^{-f(t)})dt}$

($W_n$ is the time of the nth ocurrence in the Poisson Process)

Any suggestions on where to begin? This is an optional problem of my introductory Stochastic Processes class, so maybe is a bit too theoretical for me, but at least I would like to see how to solve it.