On sampling of stationary increment processes

Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(.).1 at which a stochastic process with stationary increments . should be sampled, for the sampled process .(../q(.).q(.)) to deviate from . by at most ., with a given probability, asymptotically as ..0. The canonical application is to discretization errors in computer simulation of stochastic processes.