A Markov Chain's Sequence of State is fully characterized by it's birth rate l(t) (for lambda) and it's deathrate m(t) (for mu) and given an initial probability distribution P0 of the initial state. Also there is a maximum amount of states c (for capacity).
Let us say the sequence of states y(t) which is obtained by the birth-death system described above is available as measurements and also m(t), P0 and c is known.
How to get the inverse of the system and to calculate l(t) which creates y(t) given mu(t) and P0 and c?
What if mu(t) or P0 is not available anymore. Is it still possible?
