Deterministic dynamics on stationary point process in R^{d} are built upon compatible pointshifts: translation invariant mappings from each point of the process to another. When a pointshift is applied multiple times to a pointprocess it creates a sequence of distributions, namely, the distributions of point process given there is a point of the nth iteration of the pointshift at the origin. We will introduce the notion of marked stochastic pointshifts. Marked Stochastic pointshifts use not only the realization of the pointprocess to decide how to map each point of the process, but also extra information coming from enlarging the probability space through marks. Examples are provided and the discussion is motivated by an application in the field of theoretical Computer Science.
