State in Markov Chain

Description:

• State

State Accessibility

State Communication

Recurrent State vs Transient State

• For any state $i$, let $f_i$ denotes the probability that, starting in state $i$, it will reenter state $i$ eventually

Classes:

• Two states are in the same class if they communicates
• if $A\cap B\ne \varnothing$, then $A=B$
  • meaning if class $A$ and class $B$ has any state in common, they are the same class
• Identical vs disjoin class:
  • Identical class: ?
  • Disjoint class:?