Premise: I have searched the internet for the past 3 days without finding anything relevant.
The problem I want to address is the following:
I have an initial distribution D(0). I also have a certain number of sequential time updates of D (e.g D(1), D(2), ... D(100)). Is it possible to reconstruct the transition matrix of the underlying discrete-time markov process?
Colloqually speaking I want to reconstruct the transition matrix given the sequential evolution of some initial distributions (even more than one, if they are needed).
Do you know any keywords or resources to gain more knowledge on the subject? I have also seen something about dynamical systems and diffusion processes, but I don't really know which direction I should be moving in.