The Annals of Applied Probability

On sampling of stationary increment processes

J. M. P. Albin

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 4 (2004), 2016-2037.

First available in Project Euclid: 5 November 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60G70: Extreme value theory; extremal processes
Secondary: 60G15: Gaussian processes 68U20: Simulation [See also 65Cxx]

Fractional stable motion Lévy process sampling self-similar process stable process stationary increment process


Albin, J. M. P. On sampling of stationary increment processes. Ann. Appl. Probab. 14 (2004), no. 4, 2016--2037. doi:10.1214/105051604000000468.

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