On sampling of stationary increment processes

Abstract

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