0

I understand that a Markov Chain is reducible if, given its transition matrix $P$, there exists $n$ such that every element of $P^n$ is greater than 0.

However, I am wondering that if there is an fast and practical way to detect a Markov chain is regular numerically.

Thanks.

Tom Bennett
  • 540
  • 2
    Isn't this equivalent to determining whether a graph is connected? Wikipedia says the standard algorithm is breadth-first search. – Nate Eldredge Feb 27 '15 at 03:11
  • 1
    regular, not reducible –  Feb 27 '15 at 05:24
  • 1
    In addition to the directed graph being strongly connected, it has to be aperiodic. For this (given that it is strongly connected) it is necessary and sufficient that for some states $s$ and $t$, there are walks from $s$ to $t$ with lengths that are relatively prime. –  Feb 27 '15 at 05:27

0 Answers0