A Markov process fulfills the relation:
$E[g(X_t)|F_s] = E[g(X_{t})|X_s]$
A function $h$ is harmonic iff $(h(X_t))_t$ is a Martingale.
Is any Martingale $(M_t)_t$ constructed from a Markov process $(X_t)_t$ and a harmonic function $h$ to this Markov process, such that $M_t=h(X_t)$?
That is: $\{h(X)|X$ is Markovprocess, $h$ is harmonic with respect to$ X\} \supset \{M|M$is a martingale$\}$
The question could also be stated as: Can one construct a fair game, that is not derived from a series of markovian random events.