Is there a model/technique that is able to estimate transition matrix (which would be consistent, i.e. sums of their rows would be always 1) conditional on some continuous variable X?
Let's say I have a system that can acquire one of 3 possible states (A,B,C). I have some observations and I could apply standard Markov chains. This way I can get something we could call "unconditional" transition matrix.
However, the transition probabilities (probably) depend on a continuous variable $X\in(0,1)$. The higher X is, the higher is the chance of A going to B and B going to C (C is absorption state).