First passage statistics of threshold ratios in a simple Polya Urn model

Abstract

The Simple Polya Urn Model was used to model the evolution of a two-population system. First passage probabilities were calculated for maintaining given threshold ratios. It was shown that as the initial minority population increases, the eventual exit probability increases. On the other hand, for a given initial minority population, there exists a threshold ratio for which which the exit probability is maximum. It was also shown that the first passage probability scales as t⁻² for arbitrary initial minority population and initial threshold ratio.