Representing Markov chains with transition diagrams - Kachapova, F (Science Publications, 2013)
Stochastic processes have many useful applications and are taught in several university programmes. Students often encounter difficulties in learning stochastic processes and Markov chains, in particular. In this article we describe a teaching strategy that uses transition diagrams to represent a Markov chain and to re-define properties of its states in simple terms of directed graphs. This strategy utilises the students’ intuition and makes the learning of complex concepts about Markov chains faster and easier. The method is illustrated by worked examples. The described strategy helps students to master properties of finite Markov chains, so they have a solid basis for the study of infinite Markov chains and other stochastic processes.
Keywords: Transition diagram; Transition matrix; Markov chain; First passage time; Persistent state; Transient state; Periodic state; Inter-communicating states