Poisson Processes are Infinitely Divisible. Let N be a Poisson process on S with intensity μ. Using Laplace functionals, show that for each n, there exist point processes N 1 ,...,N n that are i.i.d....

Poisson Processes are Infinitely Divisible. Let N be a Poisson process on S with intensity μ. Using Laplace functionals, show that for each n, there exist point processes N₁,...,N_n
that are i.i.d. and N d = N₁+···+N_n. This says that N is infinitely divisible.