Empirical quantile central limit theorems for some self-similar processes

DOI10.1007/s10959-013-0511-2zbMath1342.60034arXiv1308.4194OpenAlexW1975729214MaRDI QIDQ2346983

Joel Zinn, James Kuelbs

Publication date: 26 May 2015

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4194

zbMATH Keywords

fractional Brownian motionempirical processesself-similar processescentral limit theoremsempirical quantile processes

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Self-similar stochastic processes (60G18) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Convergence of quantile and depth regions ⋮ Couplings and strong approximations to time-dependent empirical processes based on i.i.d. fractional Brownian motions ⋮ Limit Theorems for Quantile and Depth Regions for Stochastic Processes ⋮ Bahadur-Kiefer representations for time dependent quantile processes

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• Uniform Central Limit Theorems
• Functional central limit theorems for processes with positive drift and their inverses
• Sums of independent Banach space valued random variables

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