The maximum-entropy median-martingale on [0,1] has the arcsine distribution as its stationary distribution, with a proof linking it to two classical arcsine laws for Brownian motion, plus a generalization of martingales to a larger class of walks.
G., Stoyanov, J., and Universio, N
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The maximum-entropy median-martingale
The maximum-entropy median-martingale on [0,1] has the arcsine distribution as its stationary distribution, with a proof linking it to two classical arcsine laws for Brownian motion, plus a generalization of martingales to a larger class of walks.