In lecture courses on stochastic processes, simple, continuous‐time Markov processes with discrete states are usually solved by deriving Kolmo‐gorov forward equations, summarizing them by a single Lagrange partial‐differential equation for a generating function, and then solving the resulting equation by means of the auxiliary equations. Students frequently find this approach confusing. The aim of this paper is to present three alternative approaches which may be employed in order to assist in the teaching of the subject, and which are frequently omitted from text books; the approach described in § 3, in particular, is not readily available. At the same time, it is hoped that students of mathematics in general will find in these processes interesting applications of mathematical methods.