On Sampling of stationary increment processes

Details On Sampling of stationary increment processes On Sampling of stationary increment processes

2005-03-24

arxiv.org/abs/math/0503554v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 2016-2037

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000468

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.

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