3.2.4 recurrent state

  1. \(f_{ii}=1\). In otherwords, the probability of reaching state \(i\) eventually, starting from state \(i\) is always certain.
  2. \({\displaystyle \sum \limits _{n=0}^{\infty }} p_{ii}^{\left ( n\right ) }=\infty \), in otherwords, since sum diverges, this means the probability to return back to \(i\) starting from \(i\) will always exist, not matter how large \(n\) is (i.e. sum terms never reach all zeros after some limiting value \(n\))