Consider a homogeneous finite state Markov chain $\{X_n\}$ with transition matrix $P$ and state set $S$ consisting of real numbers. How to choose the elements of $S$ so that $\{X_n\}$ be a martingale? My conjecture is that the set of stationary state probabilities (if they exist) can be used as a suitable $S$ iff $P$ is doubly stochastic. Can you prove or falsify this statement?
2026-04-12 01:19:07.1775956747
Create a Martingale out of a Markov Chain.
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