I'm working on a problem concerning censoring of transitions in a Markov Chain. For example, take a Markov Chain that models a counter, it goes up or down but does not stay in position. A possible censoring could be to only observe the transitions where the new number is prime or to only observe those transitions where the new number is even.
According to what I'm told, this results in a new Markov Chain, but I can't really grasp how this changes the problem that the new Markov Chain could be modeling. Do you still take into account that you somehow got in a state to be able to make that kind of transition or can I just completely ignore it and only consider the leftover transitions?