Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. Join them; it only takes a minute:

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

Let a reversible Markov process $m_{t+1}=m_t P$, where $t$ is time that has a stationary distribution $\pi$. I saw in a paper that the dual system was defined as $x_{t+1}=P x_t$. Can anyone give me some directions in order to understand how this is derived?

share|cite|improve this question

closed as not a real question by Tsuyoshi Ito, Lev Reyzin, Jukka Suomela, David Eppstein, Vijay D Jan 16 '13 at 18:48

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

That looks like the definition of "dual system". Derived from what? – Jeffε Feb 22 '12 at 23:34

Let $y_t = x_t^T$. Then, $y_{t+1} = y_t P^T$. Thus, $y$ (and therefore $x$) corresponds to the original Markov Chain run backward in time. Hope this gives some motivation towards the concept of dual chains.

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.