Topics: Stochastic Process


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.


  • Every state communicates with itself (since ; reflexive).
  • If communicates with , then communicates with (symmetric).
  • If communicates with , and communicates with , then communicates with (transitive).