Topics: Stochastic Process
(definition)
Given a Markov chain, we say that the state is accessible from the state if for some .
Do note that we can have the case of not having the state being accessible from the state , but having the state accessible from .
When both cases are satisfied (i.e. accessible from , and accessible from ), we say that both states communicate.
We can partition the set of states in a given chain by grouping them into classes, each one containing states that all communicate.
Properties
- Every state communicates with itself (since ; reflexive).
- If communicates with , then communicates with (symmetric).
- If communicates with , and communicates with , then communicates with (transitive).