On sampling of stationary increment processes

2004/11/01 by J. M. P. Albin, J.M.P. Albin · 1 citation
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Stochastic processes and financial applications #math.PR #msc:60G10 #msc:60G15 #msc:60G70 #msc:68U20.

paper · pdf · doi:10.1214/105051604000000468

published as Annals of Applied Probability 2004, Vol. 14, No. 4, 2016-2037 · Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2004/11/01 · arxiv created 2005/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On the infimum attained by the reflected fractional Brownian motion

Related

• Extreme Value Estimation for Discretely Sampled Continuous Processes
• Asymptotic properties of functionals of increments of a continuous semimartingale with stochastic sampling times
• Average sampling of band-limited stochastic processes
• Random Processes with Stationary Increments and Intrinsic Random Functions on the Real Line
• Stochastic calculus and sample path estimation for jump processes