Hitting probabilities and expected hitting times under a weak drift: on the 1/3-rule and beyond

Peter Pfaffelhuber, Anton Wakolbinger

Published 2018-01-04Version 1

When does a small drift increase the hitting probability of a boundary point / the expected hitting time of the boundary, compared to the driftless case? We analyze this for diffusion processes on [0,1] by expanding the Green function. In this way, in the appropriate diffusion approximation setting, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and effects of stochastic slowdown (Altrock and Traulsen, 2009).