One important parameter in stationary point processes is the autointensity function. The autointensity function, hNN(t, v), of the process N(t) is the conditional probability that a point occurs at time t + v, given that a point occurs at time t. Specifically, hNN(t, v) = P[dN(t + v) = 1|dN(t) = 1]

dv where dN(t) =



1 if a point in (0, 0 + dt)

0 otherwise Show that for a Poisson process the autointensity function is a constant.

(Note: This demonstrates the nonpredictability of the Poisson process.)