Dynamic transition probability matrix in markov chains

[pyrole]

I am intrigued by the idea of changing/dynamic transition probability matrix instead of the assumption of constant transition probability between states.

For eg. Probability of population migrating between 2 states might not remain constant and can be a function of its population or some other factors. Is there a systematic study of this particular category of dynamic or changing transition probabilities in markov processes.

[Stephen Tashi]

You're interested in a topic called "non-homogeneous Markov chains" or "time non-homogeneous Markov chains".

I don't know a good reference that introduces this topic and I don't claim to be able to introduce it myself!