=+23.7. Suppose that X1, X2 ,... are independent and exponentially distributed with parameter @, so that (23.5) defines a Poisson process (N,). Suppose that Y1, Y2 ,... are independent and identically distributed and that o(X ,, X2 ,... )

and o(Y), Y2 ,... ) are independent. Put Z, = Ex NYA. This is the compound Poisson process. If, for example, the event at time S ,, in the original process represents an insurance claim, and if Y ,, represents the amount of the claim, then Z, represents the total claims to time t.