“An Empirical Transition Matrix for Non-Homogeneous Markov Chains Based on Censored Observations”, Odd O. Aalen, Søren Johansen1978 (; backlinks; similar)⁠:

A product limit estimator [the Aalen-Johansen estimator] is suggested for the transition probabilities of a non-homogeneous Markov chain with finitely many states. [competing risks survival analysis]

The estimator is expressed as a product integral and its properties are studied by means of the theory of square integrable martingales.

[Keywords: Markov chains, censored observations, product limit estimator, transition probabilities]