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On Sampling of stationary increment processes

Research paper by J. M. P. Albin

Indexed on: 24 Mar '05Published on: 24 Mar '05Published in: Mathematics - Probability



Abstract

Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi by at most \epsilon, with a given probability, asymptotically as \epsilon \downarrow0. The canonical application is to discretization errors in computer simulation of stochastic processes.