Kolmogorov's differential equations for non-stationary, countable state Markov processes with uniformly continuous transition probabilities

1. Summary We shall consider a non-stationary Markov chain on a countable state space E. The transition probabilities {P(s, t), 0 ≤ s ≤ t <t0 ≤ ∞} are assumed to be continuous in (s, t) uniformly in the state i ε E.