  Stationary stochastic processes with independent increments, of which the
Poisson process is a prominent example, are widely used to describe real world
events. With the basic assumption that a counting process is stationary and has
independent increments, here I derive two integral equations to capture the
time evolution of any such process. In order to solve these two integral
equations explicitly, I need to introduce one more restriction condition. For
sake of simplicity, I have imposed the Poisson condition on the two equations
and successfully reproduced the renown Poisson results. The methods proposed
here may also be applicable for investigating other stationary processes with
independent increments.
