Absorbing Markov Chains
Paul Aurelian Gagniuc · 2017
A classic illustration for understanding the absorbing state of a Markov chain consists in a simplistic timeline simulation of a living creature. A creature can be described by using many states. The creature can have a transition from "sick" (state "A") to "dead" (state "C"). Thus, the "dead" (state "C") state is the absorbing state for this chain. Depending on the organism and the environmental conditions, the likelihood of moving from "healthy" to "sick" or from "sick" to "healthy" or from "sick" to "dead" may carry different transition probabilities. This chapter considers the timeline simulation of a living creature that is modeled by analyzing a special configuration of jars and balls. A Markov chain is irreducible if all states communicate with each other. So far the main theme was about irreducible Markov chains. Known transition probability values are directly used from a transition matrix for highlighting the behavior of an absorbing Markov chain.