Abstract: Dynamics on stationary point process in \mathbb{R}^d are built upon compatible point-shifts: translation invariant mappings from each point of the process to another. When a point-shift is applied multiple times to a point process it creates a sequence of distributions, namely, the distributions of point process given there is a point of the nth iteration of the point-shift at the origin. Then one can study the orbit and the omega-limit set of this sequence. We will introduce the notion of marked stochastic point-shifts. Marked Stochastic point-shifts use not only the realization of the point-process to decide how to map each point of the process, but also extra information coming from marks of the point process. Examples will be provided with emphasis to an application of stochastic marked point-shifts to theoretical Computer Science.