Point processes on the positive real axis which are positively
self-exciting in a sense expressed by their martingale dynamics are studied in
this paper. It is shown that such processes can be realized as increasing
mappings of Poisson processes and are therefore associated in appropriate
manners. Some examples are presented, including Hawkes, renewal,
Pólya-Lundberg, Markov dependent, semi-Markov, in addition to other point
processes. As corollaries an extension of the Burton-Waymire association
result and a solution of the Glasserman conjecture are obtained. Some results
on dependence in stochastic processes of interest in queueing are given as a by
product.