Stochastic revision opportunities in Markov decision problems

We extend Markov Decision Processes to situations where the actions are binding and cannot be changed in every period. Instead, the decision maker can revise her actions at random times. We consider two slightly different models. In the first, the revision opportunity appears at a specific stage at which the decision maker can change her action, but is lost if not used. The action taken then remains constant until the next revision opportunity comes up. In the second model, the revision opportunity remains open and can be used at any time after it appears. Only when the action is changed, it becomes binding again for another random period. We compare between different stochastic revision processes and characterize when one is always preferred to another.