Mean-reverting random walks

Ensino Médio::MatemáticaMany financial or economic processes can be modeled as mean-reverting random walks. Mean-reverting walks differ from simple diffusion by the addition of a central expectation, usually growing with time, and a restoring force that pulls subsequent values toward that expectation. The random term is lognormally distributed, and the initial value of the mean can be above or below the series start. The strength of the restoring force is given in terms of the time to return to the mean. The plot shows sample paths which result in the 90th, 70th, 50th, 30th, and 10th percentiles in endpoint value, out of a larger sampl