  The Poisson additive process is a binary conditionally additive process such
that the first is the Poisson process provided the second is given. We prove
the existence and uniqueness of predictable increasing mean intensity for the
Poisson additive process. Besides, we establish a likelihood ratio formula for
the Poisson additive process. It directly implies there doesn't exist an
anticipative Poisson additive process which is absolutely continuous with
respect to the standard Poisson process, which confirms a conjecture proposed
by P. Br\'emaud in his PhD thesis in 1972. When applied to the Hawkes process,
it concludes that the self-exciting function is constant. Similar results are
also obtained for the Wiener additive process and Markov additive process.
