Do time-varying transition matrices exist?

[y***@somehost.somedomain]

Suppose that a transition matrix P of nxn contains the transition
probabilities between n states, we know that the probability for state i
to state j after time t is P^t. By doing so, we assume that the
transition matrix remains the same. In reality, different time (months,
for example) should have different transition matrices.
Is it possible that P1 is the transition matrix at t=1, P2 is the
transition matrix at t=2 and so on such that the probability for state i
to state j after t=5 is P1*P2*P3*P4*P5?
Please let me know if any books or articles discuss this subject.
Thank you very much for your help.
Lee

[W. Dale Hall]

Post by y***@somehost.somedomain
Suppose that a transition matrix P of nxn contains the transition
probabilities between n states, we know that the probability for state i
to state j after time t is P^t. By doing so, we assume that the
transition matrix remains the same. In reality, different time (months,
for example) should have different transition matrices.
Is it possible that P1 is the transition matrix at t=1, P2 is the
transition matrix at t=2 and so on such that the probability for state i
to state j after t=5 is P1*P2*P3*P4*P5?
Please let me know if any books or articles discuss this subject.
Thank you very much for your help.
Lee

Google "non-homogeneous Markov chain"

I'm no expert, but it seems to be what you're after.

Dale