On the Chapman—Kolmogorov equation
J. F. C. Kingmán · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · 1974
Abstract In the form considered in this paper, the Chapman-Kolmogorov equation connects a doubly infinite collection of functions, and imposes complex constraints on each of them. The main theorems characterize the functions which satisfy these constraints, and generalize known results in the theory of continuous-time Markov chains.