Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have been looking over my notes for Markov chains, and I have come across the following:

Theorem: An irreducible Markov chain is transient iff for some state $i$ there exists a nonzero vector $y$ such that $y_j = \sum_{k\neq i} p_{jk}y_k $, for all $j\neq i$ and $|y_j| \leq 1$for all $j$.

Could you please explain why this is true? I hope to gain some intuition into the result.

Many thanks.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.