Recurrent State

Description:

• The $i$ is Recurrent State if $f_i=1$, ${\sum }_{n=1}^{\infty }{P}_{ii}^n=\infty$
  • if it will go back to itself eventually
  • and it can go back to itself infinite time
  • Meaning a state starts in recurrent class, it will be in recurrent class after infinite time
• If $i$ is Recurrent State and it communicates with state $j$, then state $j$ is recurrent
  • implies that 2 states are transient if they are in different class
  • implies that all states in a irreducible Markov chain are recurrent

Positive recurrent

Null recurrent