A time non-homogenous Markov Chain is one in which the transition probabilities are not constant over time. A non-linear Markov Chain is a model that is not linear in parameters and satisfies the Markov property (independence of future and distant past conditional on present/recent past).
(1) What is the relationship between time non-homogeneity and non-linearity of a Markov chain? (2) If time non-homogeneity and non-linearity are identical, please provide an intuitive, real world, example of such a Markov Chain process. If they are different types of Markov chains, please provide an intuitive, real world example of each.