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?
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closed as not a real question by Tsuyoshi Ito, Lev Reyzin, Jukka Suomela, David Eppstein, Vijay D Jan 16 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, see the FAQ.
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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. |
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