# Thread: Interpretation of the fundamental matrix of Absorbing Markov Chain

1. ## Interpretation of the fundamental matrix of Absorbing Markov Chain

Hello!

I am studying the Absorbing Markov Chain theory, and I have a question about how to interpret the fundamental matrix (N). It is defined as the average number of times transient state j is encountered in the transition from transient state i to an absorbing state, but many times the values of N are not integer numbers. So, how should I interpret a N values of 0.2 or 1.8 for example? Should I just round it to the nearest integer? I have read many examples but in non of them this fraction number are explained.

2. ## Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

Can you give an example of a problem in which the entries of such a matrix are not non-negative integers? If it were not for that "1.8" I would suspect that the entry in the "i,j" position is the probability of transition from state i to state j rather than the "number of times" the transition occurs.

3. ## Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

Thanks for your answer, but no, this matrix gives the number of times a state is reached, and it is based on the transition matrix that gives the probability of the change of state.

4. ## Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

Margodoy, you said yourself: "the average number of times". Averages (expectations) are rarely round numbers. If the expectation is 0.2, then the interpretation is: in most random scenarios there is 0 or 1 visit to transient state j before absorption, with the probability of 0-visit scenarios being roughly 80%. As uninspiring as this statement is, there is nothing more to say.

Thanks a lot