The point process approach for fractionally differentiated random walks under heavy traffic

DOI10.1016/J.SPA.2012.08.008zbMath1264.60026OpenAlexW2007797897MaRDI QIDQ713216

Philippe Barbe, William P. McCormick

Publication date: 26 October 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2012.08.008

zbMATH Keywords

heavy trafficpoint processPoisson processFARIMA processfractional random walk

Mathematics Subject Classification ID

Applications of statistics to economics (62P20) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Fractional processes, including fractional Brownian motion (60G22) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25) Stable stochastic processes (60G52) Limit theorems in probability theory (60F99)

Cites Work

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• Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution
• Linear bounds on the empirical distribution function
• Tail probabilities of subadditive functionals of Lévy processes.
• Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution
• Stochastic-Process Limits
• Upper and lower class sequences for minimal uniform spacings
• Π-Regular Variation
• Heavy-Tail Phenomena
• Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems

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