How to estimate the transition probabilities for a Markov Chain when time intervals are non-equally spaced I've been given a dataset with a number of observable states. I am trying to apply a Finite State Markov Chain to model the system, but I found that I can't estimate the transition probabilities if the observed states were sampled using different time intervals. How can I find these probabilities?

I will try to make the question a more clear. I have samples collected in random intervals during a 6-month period. This samples represent the "quality" of a system, which is ranked from 0 to 15 in discrete intervals i.e. (0,1,2...15). I need to model de system using a FSMC to mimic the system's behavior. So far, I have estimated the transition probabilities between states using only the frequencies of those transitions using all the samples. I am not interested in modeling the time, however, I am not sure If I can estimate the transition probabilities in such a simple way or if I have to take the time between samples (which in my case is random) into consideration when estimating those probabilities.
With the limited information that you have given, it is not possible to judge the trade-off between different approaches of handling time here. I can propose the following alternatives.


Check if you can discretize the time information and then use transition to same state assumption. For example, let us say that transition from A to B took place at 30 minutes. If you have standard time interval of 10 minutes, you can say that for interval 1 &amp; 2 (10 minutes, 20 minutes), the transition was from state A to A whereas in the third interval the transition was from A to B. There will be problems though when multiple transitions take place in a given interval. You can either make the interval small enough or distribute the transition probability equally in such case.
Is the time information significant to whatever that you are trying to model? Otherwise you can ignore the time information.