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The use of coordinate processes for the modelling of impulse control forgeneral Markov processes typically involves the construction of a probabilitymeasure on a countable product of copies of the path space. In addition,admissibility of an impulse control policy requires that the random times ofthe interventions be stopping times with respect to different filtrationsarising from the different component coordinate processes. When the underlyingMarkov process has continuous paths, however, a simpler model can be developedwhich takes the single path space as its probability space and uses the naturalfiltration with respect to which the intervention times must be stopping times.Moreover, this model construction allows for impulse control with randomeffects whereby the decision maker selects a distribution of the new state.This paper gives the construction of the probability measure on the path spacefor an admissible intervention policy subject to a randomized impulsemechanism. In addition, a class of polices is defined for which the pathsbetween interventions are independent and a further subclass for which thecycles following the initial cycle are identically distributed. A benefit ofthis smaller subclass of policies is that one is allowed to use classicalrenewal arguments to analyze long-term average control problems. Further, thepaper defines a class of {\em stationary}\/ impulse policies for which thefamily of models gives a Markov family. The decision to use an $(s,S)$ orderingpolicy in inventory management provides an example of an impulse policy forwhich the process has i.i.d.~cycles and the family of models forms a Markovfamily.

On the Modelling of Impulse Control with Random Effects for Continuous Markov Processes