Stochastic three-state model with delay (Q696696)

A three-state discrete-time stochastic process with delay is studied. The optimal choice of the transition probabilities results in the cyclic structure of sample trajectories. This can be referred to as stochastic resonance. The model is analyzed with respect to the residence time hystograms \(h(u)\) for the system to be in each state for \(u\) consecutive steps. Finally, the model is applied to predict the yen-dollar currency exchange dynamics. See also \textit{T.~Ohira} and \textit{Y.~Sato} [Phys. Rev. Lett. 82, No. 14, 2811-2815 (1999)].