This exercise asks you to prove that the Poisson process conditioned to be equal to n at time 1 has the same law as n times the empirical process. Here is the precise statement. Suppose Pt is a...

This exercise asks you to prove that the Poisson process conditioned to be equal to n at time 1 has the same law as n times the empirical process. Here is the precise statement. Suppose Pt is a Poisson process with parameter λ > 0. Let Q be the law of
  conditioned so that P₁
= n. Thus Q is a probability on D[0, 1] with

Since (P₁
= n) is an event with positive probability, there is no difficulty defining these conditional probabilities. Prove that Q is also the law of
  where F_n
is defined in Section 35.3.

Chapter 36