2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74644Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(ε)^{-1} at which a stochastic process with stationary increments ξshould be sampled, for the sampled process ξ(\lfloor\cdot /q(ε)\rfloor q(ε)) to deviate from ξby at most ε, with a given probability, asymptotically as ε\downarrow0. The canonical application is to discretization errors in computer simulation of stochastic processes.Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G10, 60G70 (Primary) 60G15, 68U20. (Secondary)text